EA042786B1 - METHOD AND TOOL FOR SEARCHING OR COMPARING POINTS USING ROUTES OR ROUTE LENGTHS BETWEEN POINTS AND PLACES IN TRANSPORT SYSTEM - Google Patents

Description

Cross-references to related applications

This application is based on the following applications and declares the following invention priorities:

[A country] [Application number] [Date of application] USA 62/632.419 February 20, 2018 USA 62/758.710 November 12, 2018 USA 62/780.268 December 16, 2018 USA 62/800.428 February 2, 2019 USA 16274242 February 13, 2019

included in this application by reference.

Prerequisites for the creation of the invention

This invention is related to the search or comparison (searching or comparing) points. Traditionally, the goal of the search is to find any point (site) from a number of possible options that meet optimization problems, namely, minimizing the length of the route (route length) based on a certain need for movement between the point and the place, and also taking into account the desired characteristics of the desired point. For example, when searching for real estate, knowing the required destinations of commutes and the characteristics of the property (real estate property), the goal may be to compile a list of properties with the desired characteristics and the shortest travel time to the place work and back. Another goal may be to compare some real estate objects by the time spent on the way to the place of work and back [002].

Brief summary of the invention

Embodiments of the invention include a method (method) for searching or comparing points, a computer system that uses and implements this method, as well as a computer service that receives (receives) search and comparison requests from users and returns them responses (responds) in the form of information (information) about points and routes [003].

Depending on the embodiment of the present invention, a method for searching or comparing points along paths or path lengths is provided. The method uses complex pre-processing to precompute and store in the database the routes or route lengths between each point and representatives (representatives) within the boundaries of the transport system. The method offers a basic platform (framework) for searching or comparing points. When a request containing a route specification is received, the database contains pre-calculated data that allows you to quickly calculate the route or route length for each point. Points can be searched or compared by paths or path lengths.

Depending on the embodiment of the present invention, a computer system is provided for searching or comparing points along routes or route lengths. The system is a hardware-software complex. The complex receives data about the transport system and points from one or more data providers (data providers). The system builds graphs that model the movement between points and representatives within the boundaries of the transport system. The system calculates graph paths and stores the graph arm or graph arm lengths. This allows you to quickly calculate routes or route lengths for each point upon request, and also search or compare points by route or route length.

Depending on the embodiment of the present invention, a computer service is provided for searching or comparing points along routes or route lengths. The service allows the user to set the parameters of a search or comparison query through the user interface on any device, for example, using a smartphone. The request contains a route specification and a filtering condition. In response, the service returns the points that meet the filter condition, along with the routes or route lengths for the corresponding points, or the service compares the points by routes or route lengths [006].

The speed of calculating the length of the route for each point is of fundamental importance. The authors have compiled a mathematical proof. Let's consider some way of searching or comparing M. We can come up with such a user request (adversarial request) that M would return any list of points in a given order. The user (adversary) has two mechanisms:

(1) submit a request containing a route specification, from which an ordered list of points along the length of the route will be created; the order is set by the user; and (2) submit a query setting a point filter condition that matches a subset of points selected by the user. Thus, M must return an ordered list of points arbitrarily chosen by the user at the time of the request. The details of deriving evidence are outside the scope of the patent application.

The method, computer system and computer service all together perform tasks that are not unified and not fully implemented in known technical solutions. Previously known

- 1 042786 new technical solutions include patent US 8417409 B2; continuation of US 8738286 B2; subsection US 8756014 B2; KR 10-1692501 B1; continuation of patents PCT/KR2016/01083; WO 2017/065431A1; US 2018/0232824 A1; and KR 10-1905593 B1.

The embodiments of the invention presented here are illustrative; they are not exhaustive. People with basic technical knowledge will well imagine numerous modifications and implementations that do not violate the general structure and essence of the implementation of the invention.

In this presentation, the terms first, second, given, indicated, and the like are not used in a highly specialized sense, but are used only for distinction, unless otherwise clearly indicated by the context. A term in the singular includes plural forms, unless otherwise clearly indicated by the context. The terms having, including, consisting, and the like indicate the presence of components or characteristics, without limiting the possibility of the presence or addition of other components or characteristics.

Brief description of schemes

The diagrams included in the disclosure of the invention serve as an illustration of the characteristics and advantages of certain embodiments of the invention.

Fig. 1 shows an example of the color scheme of travel time on routes to and from the place of work, depending on the embodiment of the invention; caption: An example of colorization of travel time on routes to and from work for real estate objects with two routes to work: property ^geo.0.0^geo.0.1 ^property and real estate^geo.1.0^property. The authors used a map fragment on the Google core, any other one can be used instead.

Fig. 2 shows an example data preprocessing and storage circuit diagram depending on the embodiment of the invention, caption: Data preprocessing and storage circuit example.

Fig. 3 shows an example of a query response circuit diagram using stored pre-processed data depending on an embodiment of the invention; signature: An example of a concept for responding to a request using stored preprocessed data.

Fig. 4A-4E show an example of calculating travel time to and from a job site depending on an embodiment of the invention; caption: An example of calculating travel time to and from work.

Fig. 5 shows an example of sections on a graph of a public transport system for precalculating the shortest arm of the graph, depending on the embodiment of the invention; caption: An example of sections on the graph of the public transport system for the preliminary calculation of the shortest arm of the graph.

Fig. 6 shows an example of a table/vector storage of precalculated shortest travel time values depending on an embodiment of the invention; caption: An example of a tabular/vector storage of precalculated shortest travel times.

Fig. 7 shows an example of the decomposition of the route to the place of work and back, depending on the embodiment of the invention; caption: An example of a route to work and back H^W ₁ ^W ₂ ^W ₃ ^Wa^H, decomposed into a part tied to houses (in green) and into a part not tied to houses (in black) ), on the example of three houses as places of residence H1, H2 and H ₃ .

Fig. 8 shows an example of calculating the shortest travel time from the starting point of the route to the place of work and back, depending on the embodiment of the invention; caption: An example of calculating the shortest travel time from the starting point of the route to the place of work and back.

Fig. 9 shows an example of calculating the shortest travel time from the end point of the route to the place of work and back, depending on the embodiment of the invention; caption: An example of calculating the shortest travel time from the end point of the route to the place of work and back.

Fig. 10 shows an example of a language for describing algorithms (pseudocode) for calculating the shortest travel time from the starting point of the route to the place of work and back, depending on the embodiment of the invention; caption: An example of a language for describing algorithms for calculating the shortest travel time from the starting point of the route to the place of work and back PathFromHomeDurations (^W).

Fig. 11 shows an example of a circuit diagram of a computer system depending on an embodiment of the invention; caption: An example of a circuit diagram of a computer system for precalculating and storing data in a database, as well as processing queries using data retrieved from the database.

Fig. 12 shows an example of a user request and response from a computer service on a user's smartphone, depending on an embodiment of the invention; caption: Example of use

- 2 042786 request and response from a computer service on the user's smartphone.

The diagrams are for illustration purposes only. Explanations of the invention can be given in other diagrams without violating the principles of the invention, which can be easily understood by any person with basic technical knowledge.

Detailed Description of the Invention

Detailed description.

The invention addresses the general case of searching or comparing arbitrary points in order to obtain their optimized options at the request of the user based on routes or route lengths (routes or route lengths) to arbitrary places. At the same time, in order to simplify the presentation, the authors demonstrate the invention, first of all, on the example of specific points (sites), which are real estate objects, specific places (places), which are places of work, as well as a specific optimization goal, namely, minimizing travel time from real estate to workplace and back. The illustrative example is not exhaustive. In the last sections, we have described the principle of operation of this method in the general case [013].

1. Real estate objects and routes to and from the place of work.

Finding housing is a difficult task. People spend considerable time and material resources on its search. This technology is designed to help people find housing. There are several Internet services, the so-called property listing aggregators, that allow people to search for properties directly in their computer browser or smartphone application by certain characteristics, such as price, geographic location, number of rooms, etc. The result of the search is a certain list of options that the client, as a rule, looks at in person directly on the spot.

Location is perhaps the most important criterion for choosing a property, it is not for nothing that real estate agencies use such characteristics as a good area, convenient location, developed infrastructure, etc. The present invention is built around this characteristic.

Clients will need to commute to work, school, or other locations. Travel time along these routes determines the value of a particular property for each specific client. In addition, there is a common interest for all customers in large cities both in saving travel time, which could be freed up for more productive activities, and in saving the effort to overcome heavy city traffic. This invention helps to meet both general and personal needs.

For a simple example, imagine a family of two living in the capital of South Korea. One of the family members works as a civil servant in the city government, and the other works as a librarian at the Main Library of Seoul National University. They now live in a two-room apartment of 69 m ² with one bathroom, the required deposit for which is 350,000,000 KRW. The apartment has latitude and longitude coordinates (37.5333, 127.0746). The total time of their daily trips to and from work is 1 hour 41 minutes (about 25 minutes one way on average). But it turns out that they can reduce the travel time to 1 hour 16 minutes (saving 25 minutes) if they move to another apartment with the same parameters, but located at coordinates (37.5041, 126.8888). The shortest travel time for both apartments is 50 minutes. But the new apartment has a different price and size (illustration dated February 19, 2018) [017].

What is the difficulty of such optimization for everyone? It is quite primitive to consider separately each version of a property on the market that meets the requirements of a family in terms of size and other characteristics, and, knowing the place of work, calculate the travel time by requesting information through existing Internet route building services. This approach is still not suitable for a large flow of requests. One of the problems is a large number of real estate objects of a modern large city presented on the market. Another issue is the large number of families/users that potentially need to be optimized. Even assuming the possibility of inexpensive use of route building services, the quadratic nature of the problem will still mean an increase in the cost of the total volume of requests to such services.

How can you meet the need for optimization for everyone? This invention is the solution. The invention has the following components.

1) The invention defines a route model to and from work (commute path). This model is versatile by including a wide range of real-life routes to different places, for example, first to school, then to the piano tutor, and then back home. The usefulness of this model is enhanced by the fact that you can quickly find properties for which travel time is minimized.

2) The invention provides an optimization method for fast travel time calculation. The invention defines the parts of any route to and from the place of work, tied to any real estate object. The travel time for these parts is calculated in advance and stored in the database. As a result

- 3 042786 tata, when you need to find a route to the place of work and back, the invention will be able to quickly build (assemble) time segments, getting the travel time for each property.

3) An embodiment of the invention is a computer service with access via the Internet. The service enables 25 million residents of the Seoul metropolitan area to search and compare real estate by travel time.

2. Description of the method.

The authors use the term travel in a broad sense, which includes the movement of objects or data. A description of travel is a description that a person with basic technical knowledge can give. Here are some examples of movement descriptions:

(1) hey friend, you need to go one block to the north, then take a little to the left; or (2) $5 [020].

You can use the term travel path when you mean the name of a travel. The length of travel is a numeric value that a person with basic technical knowledge would be able to associate with travel, such as distance, monetary value, etc. As another example, the term travel duration can be used when referring to the length of travel expressed in time. The length of the move is itself a description of the move. The move description cannot include any move length, but may only include a specific move length or also some other data.

The authors demonstrated some of the possibilities of the method and introduced the terminology that will be used in the future. The method can calculate the travel time for routes to and from work for each property. This is shown in FIG. 1. The city area is divided into colored squares. The color indicates how long it takes to travel by public transport from a particular property in a particular area: green indicates the shortest route, yellow indicates the longer route, and red indicates the longest route. The route to and from work starts from the property, then goes to certain locations geo, ..., and finally returns to the original property again. To some extent, a real estate object is a free variable, while geo, ... are fixed variables. In FIG. Figure 1 shows two routes to and from work: a non-closed route of the type real estate^geo.0.0^geo.0.l^property twice a week, and a forward and backward route of the type real estate^geo.1.0^property three once a week. As you can see, given these two routes to and from work, as well as their regularity, properties with a small weighted sum of travel times form a kind of blob (dark green), which is not surprising, given the density of the public transport network.

At the highest level, the method consists of two parts. The first part calculates the travel time between properties and representatives, which are stops in the transportation system. This travel time is stored (stored) in the database (database), and it can be taken ready-made when a request arrives (request). See fig. 2 for illustration. The second part is processing requests. The request contains the route to the place of work and back, as well as the desired characteristics (features) of the property. When a received request is received, the corresponding travel time is taken from the database and used along with other data to obtain the total travel time to and from work for each property with the selected characteristics. See fig. 3 for illustration. Details and variations of this description are given in the following paragraphs [022].

3. Routes to the place of work and back.

This method processes a large sample of routes to and from work, used by people within the boundaries of an urban agglomeration. The route to the place of work and back starts from point H, which the authors called the house (home). H has an arbitrary location. It can be represented by any real estate object, for example, an apartment, a rented room, a cottage with its own plot, a large enterprise, a hotel, etc. It can also be a point where the client works, for example, a restaurant, a shop, etc. But by agreement on names in disclosing the essence of the invention, the authors, as a rule, use the term house; such an agreement does not imply restrictions. In one implementation, the client travels to different locations and then returns to point H.

In one implementation, the travel route fits within the framework of one day, for example, the client leaves H in the morning and returns to H in the evening of the same day. In another implementation, the route fits within a couple of days, for example, if the client works the night shift or his work shift is 25 hours. In one implementation, any movement can start at a certain time or end at a certain time, for example at 8:00: 12. In another implementation, any movement may begin or end within a certain interval,

- 4 042786 for example in the morning.

Simply put, the client moves from H to W, which the authors call work. W has an arbitrary location. This includes school, grandparents' home, weekend golf course, favorite restaurant, doctor's office, place of worship, and so on. It can also be the place where the person lives. But by agreement on the names in the disclosure of the essence of the invention, the authors, as a rule, use the term work; such an agreement does not imply restrictions. The client then returns from W to H. The authors refer to these two movements as a forward and reverse route. See fig. 4A for illustration.

An open-loop route to and from work is an example of a more complex route to and from work. See fig. 4B for illustration. With this route, the client moves from H to place W1. After that, the client moves from location W1 to another location W2. Finally, the client moves from W2 back to H. One example is when the client goes to school and after school goes to the piano tutor.

In general, this method allows any arbitrary movement. In FIG. 4C shows an illustration of a route to and from the job site skipping W ₄ to W2 and repeating W2 to W ₃ . In FIG. 4D shows an illustration of non-closed routes to and from work: a route to and from work leaving H but not returning to H; and the route to the place of work and back, with a return to H without first exiting H. FIG. 4E is an illustration of an unrelated route to and from a job site. The route to the place of work and back can start from one house and end in another house. this method determines the route to the place of work and back as follows.

Definition 1. The route to the place of work and back is a set of movements W ₂ ^W ₃ , W4^W ₅ ,—, W _k-2 ^W _k-1 , with k>2, which is considered an integer, including H _re p _BY ^W ₁ or W _k ^ _{N next} (thus, the route to the place of work and back always contains at least one home and at least one place of work), carried out at arbitrary times.

The route to and from the place of work can be represented as a specification of the route within the boundaries of the transport system. The various W and H in definition 1 indicate the direction for the client to move [028].

In one of the implementation options, the authors consider a simpler route to the place of work and back H^W ₁ ^W ₂ ^...^W _k ^-H, for any k>1, the end points of movement along this route will intersect, and the house at the beginning and at the end of the route is the same. In disclosing the essence of the invention, the authors use, as a rule, a simpler form, since it is the most frequent in practice and simplifies the understanding of the presentation. At the same time, it is obvious to any person with basic technical knowledge that this method is applied to the author's (basic) determination of the route to and from the place of work.

This method finds the shortest travel time on any of the routes to the place of work and back. In itself, this has already been reflected in various known technical solutions. But this method finds the travel time for all the houses in an extremely short time.

4. Pretreatment of the transport system.

The method pre-processes public transport system data to precompute and store the shortest travel time for all homes.

4.1. Calculation of the shortest travel time.

The authors describe a way to efficiently calculate the shortest travel time between all homes and all public transit locations. As a rule, in the disclosure of the essence of the invention, the authors use the term stops (stopstations) for public transport stops, which include bus stops, metro stations, or both of these modes of transport at once.

The method begins with the construction of an arbitrary graph (graph) of the GT public transport system, which models the public transportation system and which can be taken from known technical solutions. The graph may contain vertexes that represent bus stops, subway stations, or both. Other vertices may also be present on the graph, meaning, for example, the place where vehicles stop or turn around, or the place where pedestrians stop or turn. The vertices on the graph corresponding to the places of transport stops are denoted

STOPSTATIONs, with index s. The graph has directed weighted edges, each of which represents the travel time along the segment from the source edge vertex to the target edge vertex. The graph can also have other edges. An edge can denote a segment of a transfer route between different transport routes. The graph may contain data on the departure time or arrival time of different public transport routes. As a rule, Dijkstra's algorithm is used to find the shortest graph arm from one vertex to all the others (shortest graph

- 5 042786 paths) or the search algorithm A* (A star) for calculating the path from one of the vertices of the graph with the shortest arm of the graph (sum of weight values), denoting the shortest travel time from one

STOP STATION s' to another

STOP STATIONs, for any s' u s, and if the movement starts at the specified time or ends at the specified time [033].

This method extends the graph of the public transport system GT. See fig. 5 for illustration.

First, the authors introduce clusters of stops (clusters of stopstations). The method groups stops into clusters using some clustering algorithm; in one implementation, the method groups two stops into one cluster if the geographic distance between the two stops does not exceed a threshold value (threshold), for example, 5 m, or if the travel time between two stops does not exceed the threshold value. The authors talk about the location of the cluster, referring to some geographic location within the boundaries of the cluster, such as its central point. For each cluster of stops with this method adds two vertices

STOPSTA TIONCL USTERSO URGE_s and

STOPSTATION CL USTER TARGET c, as well as edges connecting the cluster with GT stops

STOPSTATION CLUSTERSOURCEc -+ STOPSTATION s' marked FirstWaitGetOn and

STOPSTATION s'-+ STOPSTATION_CLUSTER TARGET c marked Zero, for any s', always when s' is in cluster c. Edges have zero weight. The resulting graph is denoted GC with vertices VC and edges EC. Subset of vertices

STOPSTATION CL USTER SO URCE c, denoted by VS [035] for all c.

Another extension is house clusters. The method groups houses into clusters according to some clustering algorithm; in one implementation, the method uses the same algorithm as when clustering stops. The location of a cluster of houses is determined in a similar way. For each cluster s, the method introduces a vertex

HOMECL USTERSOURCEs and top

HOME CL USTER TARGETs

[036].

labeled Walk if there is a walking segment in the opposite direction from the location of the cluster of stops c to the location of the cluster of houses t, for any c and t, while the weight of the edge reflects the travel time along the walking segment. In one of the implementation options, the method limits walking movements to the shortest sections at a given speed, for example, 4 km / h, with a duration not exceeding a threshold value, for example, 1 hour. The resulting graph is denoted G. The authors assigned the designation VH to the vertices

This method connects each cluster of houses with clusters of stops in the form of walking sites. In particular, the method adds an edge

HOME CLUSTER SOURCEs -+ STOP STATION CLUSTERSOURCE_c with the flag Walk if there is a walkable segment from the location of the cluster of houses s to the location of the cluster of stops c, for any s and c, while the weight of the edge reflects the travel time along the walking segment; and inverted rib

STOPSTATION CLUSTER TARGET with -+ HOME CLUSTER TARGETJ marked Walk if there is a walking leg in the opposite direction from the location of the cluster of stops c to the location of the cluster of houses t, for any c and t, with the weight of the edge reflecting the travel time along the walking leg. In one of the implementation options, the method limits walking movements to the shortest sections at a given speed, for example, 4 km / h, with a duration not exceeding a threshold value, for example, 1 hour. The resulting graph is denoted G. The authors assigned the designation VH to the vertices

HOMECLUSTERSOURCEs, for all s; and the notation EN - to the set of edges

HOME CLUSTER SOURCE s -+ STOPSTATION CLUSTER SOURCE s, for all s and s.

The authors are interested in calculating the shortest graph arm from each cluster of stops to each cluster of houses, as well as the shortest graph arm in the opposite direction from each cluster

- 6,042,786 houses to each stop cluster.

Note that clustering allows this method to significantly improve the quality of calculation of the shortest arm of the graph due to the unification of locations, which are essentially the same from the point of view of the shortest arm of the graph. For example, in a high-rise residential complex there may be hundreds of apartments, and this method will combine them into one single cluster of houses. Thus, the algorithm for calculating the shortest arm of the graph will need to process only one cluster of houses, and not hundreds of apartments included in it.

At the same time, the typical application of Dijkstra's algorithm still does not provide high quality. In a typical application, the algorithm starts processing with each

STOP ST ATION CL USTERSO URCEc in G without any vertices

HOME CLUSTER SOURCE S after which the algorithm proceeds from each vertex

HOMECLUSTERSOURCEs in G without any vertices

HOME CL USTERTARGETJ

The cumulative asymptotic time complexity looks like

O(\vs\ (\EC\ + \EN\ + (\VC\ + \VH\} log(|VC\ + \VHJ) +

O(]VH\ · (\EC\ + \EH\ +(|LC| + |VH\) log(QQ + \EHJ).

This method improves the typical application of this algorithm. The authors noticed that in large urban areas, the number of clusters of houses significantly exceeds the number of clusters of stops |EN|»|VSI, with the same threshold for grouping into clusters. Based on this observation, this method uses a different algorithm for calculating the shortest arm of the graph from clusters of houses: in this method, the edges of G are reversed, and for each

STOP ST A TIONCL USTERTARGETc on the inverted graph, the shortest leverage to all tops is calculated

HOMECLUSTERSOURCEs using Dijkstra's algorithm (any vertices

HOMECL USTERTARGETJ can be removed). This gives the desired effect, because when the edges of any of the shortest arms are turned over from

STOP ST A TIONCL USTERTARGETc to

HOME CL USTERSOURCEs on an inverted graph get the shortest graph arm from

HOME_CLUSTER_SOURCE_s before

STOPSTA TIONCL USTER TARGETc on the original (not flipped) graph. Hence, by this method, an asymptotic time complexity of the form is obtained

O(|FS| QEQ + \EH\) + (IFC| + \VH\) log(|EQ + |EH|))).

In fact, this method offers a significant reduction in the total processing time on graph G for the Seoul metropolitan area [040].

This method uses a symmetric algorithm for the opposite situation, when the number of stop clusters exceeds the number of house clusters |VH|<|VS|. In this case, this method reverses the edges when calculating the shortest arm of the graph from clusters of stops to clusters of houses.

In one embodiment, the method uses the departure time (departure times). The method calculates the shortest graph arm from each

STOPSTA TIONCL USTERSO URCEc before each

HOME CL USTER TARGETJ, for a given departure time from

STOPSTATION CL USTER SO URCE c.

In this case, the method uses the corresponding GT graph from known technical solutions, which allows you to set the departure time from public transport stops; such a case is sometimes denoted by a vertex, which corresponds to a time value and geographic location, and an edge, which denotes the travel time from the geographic location to the specified time.

- 7 042786

Similarly, the method works on an inverted graph using a given time of arrival at

STOPSTATION CL USTERTARGETc.

The lengths of the shortest arm of the graph translate these arrival times into departure times from each

HOME CLUSTER SOURCEs.

A similar graph is used to calculate the shortest graph leg based on the arrival deadline. An appropriately constructed graph can be used to calculate the probability of arriving early [042].

In one implementation, no vertices are introduced into the GT

STOPSTATION CL USTERSOURCEc no top

STOPSTATION CL USTER TARGET c.

Instead connect the vertices

HOME CLUSTER SOURCEs and peaks

HOME CL USTER TARGET J

STOP STATION s'.

In one implementation, no vertices are introduced into the GT

HOME CLUSTER SOURCE s no top

HOME CL USTERTARGETJ.

Instead, introduce vertices

HOMEs, each corresponding to a house and connected to vertices

STOPSTATIONS' EDGE HIKING SITES DIRECTLY.

In one embodiment, the houses are not grouped into clusters.

One implementation does not group stops into clusters.

In one implementation, the shortest arm of the time-of-arrival graph is calculated: from clusters of stops to clusters of houses, taking into account the time of arrival at each cluster of houses, or from clusters of houses to clusters of stops, taking into account the time of arrival at each cluster of stops.

In one implementation, the authors use some algorithms for calculating the shoulder of a graph that differ from Dijkstra's algorithm, for example, the search algorithm A* (A star). In one implementation, the authors use an approximation algorithm to calculate the shortest arm of a graph. You can use the algorithms without any improvement in the quality of the calculation.

In one embodiment, the weights on some of the graph's edges indicate the monetary cost of the move rather than the travel time. Then this method searches and compares houses based on the cost of travel to and from work. You can use any other semantic series for edge weights, such as the number of transfers between different public transport routes, waiting time, financial costs of waiting, or travel distance.

In one implementation, the authors use multiobjective optimization search based on multi-dimensional cost. For example, the shortest graph arm whose length denotes travel time is searched for, such that the monetary value that denotes the graph arm does not exceed a threshold value, or when the monetary value is added as a cost for the length of the graph arm [050].

In one embodiment, the route of movement is designated as the arm of the graph. The authors calculate various characteristics of the shortest travel route using the shortest graph, e.g. first stop (i.e. embarkation) or last stop (i.e. disembarkation) on the shortest leg of the graph, main transfer stop on the shortest leg of the graph, number transfers between different routes, the transport with the longest travel time (for example, bus 1234), the total waiting time at stops, the total distance of walking sections, the degree of congestion of a particular arm of the graph during peak hours, or the sequence of geographic locations along the shoulder of the graph. Such characteristics can be used when processing requests to filter travel routes whose characteristics match the condition specified in the request.

In one implementation, the authors calculated two or more arms of the graph between some graph vertices. For example, one arm of the graph from the vertex to the vertex v can be covered by a maximum of one bus, and on the other arm of the graph from the vertex to the vertex v there may not be a subway, but

- 8 042786 the travel time on it is only 10 minutes longer than on the shortest arm of the graph.

In one of the implementation options, the authors calculated the shoulder of the graph, which corresponds to different filter conditions (filtering conditions). For example, the shoulder of the graph, on which no more than one transfer is provided or the maximum time for overcoming pedestrian sections is set.

In one implementation, the authors use a route building service (eg, based on known technical solutions) to calculate the shortest travel time between homes and public transport stops. Therefore, in some cases, the columns described in this section 4.1 cannot be used.

The method described in section 4.1 calculates the shortest travel time from each house to each stop, as well as the shortest time in the opposite direction. The following describes a data structure for efficient storage and processing of shortest travel time data used by this method.

4.2. Storage of the shortest travel time.

In one implementation, this method stores (stores) travel time in the form of vectors (vector form). The method builds sequences of clusters of stops in the form s1, ..., sn, as well as sequences of clusters of houses in the form hi, ., h _m in some order, for example, arbitrarily. In one embodiment, such sequences become fixed. For each si, this method stores a vector of the shortest travel time from si to house clusters using a sequence of house clusters

V/ ^— (41, //,2, · · , so that the value of the vector (vector) vi at coordinate (coordinate) j, vi[j], is ti,j, equal to the shortest travel time from the stop cluster si to house cluster hj See Fig. 6 for an illustration [056].

The sequence of house clusters simplifies the calculation of the shortest travel time to each house cluster. For example, if the client needs to move from the cluster of stops si1 and further from the cluster of stops s _i2 , just add the vectors v _i1 and v _i2 coordinatewise, and the resulting sum contains the total travel time from both clusters of stops to each cluster of houses h1, ., h _m .

In one implementation, the method stores the return journey time from houses to stops using the same sequence of house clusters. Those. way store vector

V / ^- (/ /, 1, ti,2, , ti,m), so that v'iU] ⁼ t'hJ, is the shortest travel time from the cluster of houses hj to the cluster of stops si (change of variables must be taken into account; the vector v'i is used for one stop cluster, even if the movement is in the opposite direction) [058].

As a rule, two vectors for the same cluster of stops si are not equal, v,^v'i, because the minimum travel time to home may differ from the travel time from home (as a rule, the movement is not symmetrical (not symmetric) process). However, in one implementation, the method calculates and stores only one of the two vectors, and also uses it instead of the second, thereby reducing calculation time and saving space in the system. In another implementation, the method stores a weighted average of each coordinate of the two vectors, which can reduce the worst-case error. The weight values can be given as 0.5, or a route preference can be given to or from a particular cluster of houses based on, for example, the frequency of requests [059].

In one implementation, the method stores travel time rounded to the nearest whole minute using one bit of computer memory expressed as an unsigned integer from 0 to 254, with 255 indicating an unknown or too long travel time. Storing such data allows efficient addition of vectors using modern computer hardware that supports vector operations and saturation arithmetic (for example, the AVX-512/AVX-512 instruction set or the internal mechanisms of the graphics accelerator (GPU intrinsics)), while not allowing the error to go beyond a practically acceptable level of no more than 30 s and covering the values of the total travel time up to 4 hours or more. Any other rounding may be used, for example the time in seconds can be divided by 120 and rounded up to an integer, which will be expressed as time at a resolution of 2 minutes [060].

In one implementation, the method stores the vector for non-clusters. For example, some s1, ., s _n denote stops (not clusters of stops), or some h1, ., h _m denote houses (not clusters of houses).

In one implementation, this method uses a different kind of vectors to store travel time values. For example, a hash table (hash map) or a list (list) (coordinates, values). Such infrequent species may have an advantage in the case of many unknowns or too long travel times [062].

In one implementation, the method stores travel routes using vectors that follow a sequence of house clusters h1, ., h _m , or another kind of vector, such as a hash table or list (of coordinates, values). These routes can be used

- 9 042786 when processing requests to filter travel routes whose characteristics match the condition specified in the request [063].

5. Travel time on one route to the place of work and back.

The authors give a description of the efficient calculation by this method of the shortest travel time along any route to the place of work and back. Consider a route to the place of work and back, starting from the cluster of houses H, passing through job k>1 and returning to the cluster of houses: H^W ₁ ^W ₂ ^...^W _k ^H. We need to find the shortest travel time for a given route to and from the place of work from each N. Such a calculation will be quite expensive, because the number of clusters of houses can be as large as 500,000, given a radius of several meters specified for grouping into clusters. But this method offers a solution that significantly speeds up the search: this method decomposes the route to and from the place of work into a part not tied to houses and a part tied to houses, as shown in Fig. 7.

5.1. Middle part: displacement W1^W ₂ ^...^W _k .

This method finds the shortest travel time to move W1^W ₂ ^...^W _k , excluding the cluster of houses. For each segment Wi^Wi+1, this method refers to one of the routing services (for example, from known technical solutions), which calculates the shortest travel time from Wi to Wi ₊₁ using the transport system (for example, including walking sections, trips by metro and bus, transfers, or a completely walking section from Wi to Wi ₊₁ ). After that, this method adds up the values of the shortest travel time in the form of different i. The resulting amount is expressed as follows:

PathNonHomeDuration(H ^z i —> Wi —>. . . —> Wk) =

RoutingEngineShortestDuration(147 &^ ₊₁ ).

l<i<k-l

Note that only k-1 calls will need to be sent to the route building service. This number is not tied to the number of houses.

In one implementation, this method uses the departure time (departure time), arrival deadline (arrival deadline) or other parts of the request when contacting the route building service [066].

Then this method calculates the shortest travel time for the open-jaw part of the route to and from work: two segments H > W] and Wk > H, in which there is a cluster of houses. The calculation must be done very quickly, because its result will be needed for each cluster of houses.

5.2. Start part: move H^W ₁ .

This method considers two travel paths from H to W1. See fig. 8 for illustration. One of the routes provides a completely pedestrian section. If H and W1 are near by, it is often actually fastest to move completely on foot. In this case, this method refers to the route building service (for example, from known technical solutions) to calculate the shortest travel time walk (H^W1). The second way involves the use of the transport system. This method finds stop clusters (stopstation clusters) that are within a threshold reach, for example 2000 m from W1, designating them as set A. Set A is a subset {s1, .„, s _n } of all stop clusters (in Fig. 8 A={s1, _s2 , _s3 }). This method calls the walking path service to get the shortest travel time walk(s _i ^W ₁ ) for each s _i in A. If H and W1 are not nearby, often the fastest way is to travel using a stop. from set A, and then continue moving along the corresponding walking section. Due to our two-way approach, the resulting value is often the shortest travel time [068].

A two-way approach can be applied to each cluster of houses. Recall that the vector v' _i contains the values of the shortest travel time to the cluster of stops s _i from successive clusters of houses. Thus, this method calculates the shortest travel time from the cluster of houses hj by extracting the vectors v' _i from the database and using the following formula:

a.j = min{walk(Hj -> 14^), min{r [/] + walk(si -> VFjjj (Equation 1)

In one implementation, this method calculates walk(Hj^W1) only if the distance from the house cluster Hj to W1 is less than a threshold, such as 2000 m, or if the travel time from the house cluster Hj to W ₁ is less than the threshold. Denote the set of such clusters of houses as J.

In one implementation, by designating the vectors v', this method immediately calculates the travel time from each cluster of houses using vector operations (vector operations) with ν' as follows:

- 10 042786 for j = 1 to m ^a j = ^ for all 5 _; EA w = walk(s _l -> Wi) / a _r \ / min{a ₁ , r-[1] + w] \ ^a 2 \ _ min{a ₂ , V-[2] + w] j \ ^a m/ \min{a _m , v- [m] + w}/ for all j EJ w = walk(Hj -> Wi) a _} = m)^, w}.

In one implementation, this method uses the mathematical formula (mathematical formula) mm{walk(Si -> W-A + ν ], s^A where the + (operation) operation adds a number to the value at each vector coordinate, and the min operation calculates the minimum value in each coordinate over several vectors [072].

The vector (a1, ..., am) of travel time values is denoted as follows: PathFromHomeDurations(—> Wi) = (αι, ..., a _m ).

An example of an algorithm description language for calculating PathFromHomeDurations is shown in Fig. 10.

One implementation uses the uint8 number format to store aj, v'ij, or w. In one embodiment, the stored number is expressed in minutes. In one implementation, the sum v'i[j]+w for some j is performed using saturation arithmetic in the range 0 to a threshold, such as 255. In one implementation, the term v' ₁ [j] is first converted to a wider number format, such as the fp16 or uint16 formats, and only then added to w to avoid arithmetic overflow during addition. In one implementation, some of the calculations included in the mathematical formula are performed using at least one instruction for vector operations (including tensor operations), such as the AVX-512 instruction or the internal mechanisms of the graphics accelerator supported by the hardware security. In one implementation, some of the calculations included in the mathematical formula are partitioned and such sections are performed in parallel [075].

In one implementation, this method uses a nearest neighbor (nearest-neighbor) data structure, such as a KD tree for stop cluster locations, to quickly calculate set A when processing a query.

In one implementation, this method limits the set A to a value not exceeding the number of stop clusters closest to W1, for example, not more than 100.

In one implementation, this method limits the set A to clusters of stops within the walking area, not going beyond a certain distance to W1, for example, within a radius of 2000 m.

In one implementation, this method precalculates the shortest walking time from points within a threshold distance from each house cluster location to the home cluster location, or precalculates the shortest walking time from points within a threshold distance from cluster locations stops to the location of the cluster of stops. This method then does not call any walkway calculation services during query processing, but instead uses the pre-calculated walking time.

In one implementation, the shortest travel time on foot is calculated from the geodetic line, ignoring any obstacles. This speeds up the calculation of walk(si^W1) at the expense of accuracy.

In one embodiment, Equation 1 uses travel routes. For example, if a user query has a condition that limits the number of transfers between transport routes, a filter is set for si and j: the equation finds the number of transfers stored on the travel route, and if this number exceeds the specified limit, ignore the defined s _i and j in equation.

In one implementation, grouping travel times by stops si, just as it was done for v'i, improves the quality of work with the database. Indeed, despite the fact that set A depends on a user request that cannot be known in advance, for each si from set A, it is necessary to obtain an expectedly large number of travel time values.

In one implementation, the vectors v'i for the array i are randomly assigned to different processing blocks. This can reduce the waiting interval when calculating the vector (a1, ..., am),

- 11 042786 because the stops included in set A are often evenly distributed across processing units.

In one embodiment, the vectors v'i for the array i are combined into geographic processing blocks. This can improve processing speed when calculating the vector (a1, ..., am) by reducing the need for data transmission due to the fact that the set A often consists of stops located next to each other.

5.3. End part: displacement Wk^H.

The calculation is similar to the previous point, but uses the vectors v, not v'. See fig. 9 for illustration. this method calculates the set B of clusters of stops within the threshold distance from Wk (in Fig. 9, the set B=^ ₄ , s ₅ }). Thus, this method calculates the shortest travel time from the cluster of houses hj in the form

Ibj = min{walk(W _k -> Hj), min{waZk(iy _fc sj + iy[/]}j (Equation 2)

As above, in one implementation, when the vector is denoted as v, this method calculates the travel time immediately to each cluster of houses using vector operations on v according to equation 2. In one implementation, this method uses the mathematical formula min{waZ/ c(I46, -> sj 4- vj Si^B

[086].

A vector (b1, ., b _m ) of travel time values is denoted as follows: PathToHomeDurations(M ->) = (bi, ..., b _m ).

This method uses options similar to section 5.2. For example, in one of the implementation options, this method uses a vector operation that calculates the part of the vector (a _b ., am) and the vector (bi, ., bm) at once.

5.4. Combining the beginning, middle and end parts.

Finally, this method calculates (computes) the shortest travel time to and from work for each cluster of houses. This method simply adds two vectors and moves the values along the coordinates. Denote the resulting vector as

PathDurations( Wi ^> W2 ... Wk ^) =

PathFromHomeDurations(—> Wi) + PathToHomeDurations(M —>) + PathNonHomeDuration(PFi W2 ^ . . . ^ Wk), (Equation 3) where the first + means coordinatewise vector addition, and the second + means adding a number to the value at each vector coordinate [089].

In one implementation, this method calculates the travel time given a given departure time from a geographic location or arrival time to a geographic location along a route to and from a place of work [090].

In one implementation, this method precalculates the travel time PathDurations for given routes to and from work. For example, this method calculates and saves

Path From Hom eDurations(—> W) and

PathToHomeDurations(lP -►), for each W that represents a school. During query processing, this method finds precalculated vectors in the database instead of calculating them according to equation 1, equation 2 and equation 3 [091].

In one implementation, the value of PathDurations can be changed. Consider school W, which has a local residence requirement for admission, meaning that only children from certain homes can attend. This condition can be easily satisfied by setting the coordinate values of the PathFromHomeDurations(^W) vector to infinity for those clusters of houses that fall outside the boundaries of the area (zone) of registration for admission to school, and in the same way setting the coordinate values of the vector PathToHomeDurations(W^). A similar change can be made if W is an area-restricted restaurant, or a government agency that is responsible for a particular area. Values changed in this way can be saved and used when processing requests [092].

In one implementation, this method applies an arbitrary manipulation function (manipulation) to the coordinate values of the vectors vi, v'i or PathDurations. For example, this can help in the implementation of state policy to reduce the fare when moving between certain parts of an urban agglomeration in a special economic zone affected by

- 12 042786 emergency. Such a feature may be applied before the request is processed (eg, as a general policy) or during processing (eg, as a personalized policy) [093].

In one implementation, this method calculates PathDurations for a subset of clusters of houses. For example, a subset is determined by a condition of the characteristics of a house given in a user query. In one implementation, we select the sequence h1, ..., hm from clusters of houses in such a way that these subsets are often located on a short segment of the sequence, which reduces the amount of data transfer.

6. Search for one house.

This method demonstrates the efficient selection of houses along the routes to and from the place of work. Let's first show some examples of search queries before presenting a general search query for a single house.

6.1. Query with a weighted sum.

Consider a family where one parent goes to work in geo 1 five times a week and the other parent goes to work in geo2 three times a week. This family wants to find a home with the shortest weekly travel times. One can find the weekly family move times for each house cluster as a weighted sum of two vectors, namely

5 Path Durations^ geol —>) + 3 Path Durations^ geol —>).

6.2. Minimum value request.

Consider the case of a single mother who works from home and walks her child to school. She needs to find a house that is not far from any school from the set E. You can find the time of daily movements of the child for each cluster of houses in the form of a minimum coordinate-wise minimum value of the vectors, namely min PathDurations (-> e - >)

6.3. General search query for a single house.

In one of the implementation options, this method defines a request as a certain sequence of routes to and from the place of work path1, ..., pathq for any q and the function Deriver: Rq^R , which converts any vector of numbers q into any number. This method calculates travel time vectors (from starting position by extracting precalculated vectors or both)

PathDurations(/W/?i) ..., d^m),

Path Duration ) =(d _q x, , d _q ,m), and applies the Deriver function to the vectors coordinate-wise to obtain a RequestDurations(f»a/Z?i, ,.,path _q , Denver) = (Deriver(Ji_i , ..., d _q ^\

Deriver(tZi,2, ..., d _q ,i),

Deriver(Ji, _m ,..., d _q , _m ) ) with the derived travel time for each house cluster.

In one implementation, the Deriver function is a weighted sum of numbers Deriver(xi, . . ., Xq) = W]_ xi + . . . + w _q x _q , for weights w1, ..., w _q . Weight values can be positive or negative. If travel time is interpreted as a monetary cost of travel, then a negative weighting value can be interpreted as financial savings, for example, if the customer wants to save on travel on a certain route to and from work (for example, on parcel deliveries). The weights may reflect the relative importance of travel routes to and from the workplace, for example, the route to and from the workplace of the CEO may have a higher weight than the route to and from the workplace of the first line manager [099].

In one implementation, the Deriver function represents the minimum value of the numbers

Derivertxi. . ., x _q ) = min x _t l<i<q

In one implementation, the Deriver function is a weighted sum and a minimum value

Derivertxi, . . ., x _r , χ,-ι,. . ., xE = %m xi +. . . + wxr + minW; X;

r+l<i<q

In one implementation, the Deriver function is conditional, such as

- 13 042786

Deriver(xi, x ₂ ) = [ if xi < 30 then return xi + X2 else return yes], or some algorithm.

7. Comparison of two houses or more.

This method demonstrates the efficient comparison of many houses along the routes to and from the place of work. The authors show the implementation of this method with several examples before submitting a general request for comparison.

7.1. The house where you currently live.

Consider a family that lives in a certain house. Family members travel along specific routes to and from work, school, and other places. The family is considering moving to another home and wants to compare the total travel time for their current home with the total travel time for other potential new homes. This method makes such a comparison much easier.

In one implementation, the method calculates the travel time for each cluster of houses, including the cluster of houses hj of the current house S of the family

RequestDurations = (w, ..., qm).

This method returns a response containing a vector of difference (difference): this method subtracts the value of the y-th coordinate from the value of each coordinate (q-f ,..., qj-1-qj, 0, qj+1-qj , ... , _qm ~ qj).

The negative value of the coordinate of the difference vector means that the house corresponding to the coordinate has a shorter travel time compared to the current house S [105].

In one implementation, this method uses one route to and from work for the current home and different routes to and from work for other homes. Thus, this method helps the family evaluate a hypothetical scenario: Let's say we change jobs and move to some other house. How will the new travel time to and from work compare to our current travel time to and from work?

7.2. A general comparison of two or more houses.

Consider a family where both mom and dad will have to continue going to their old jobs (the job doesn't change), but the kids can change schools. Consider another example of two families: parents and maternal grandparents. They want to find two houses within 30 minutes of each other, with one house close to a hospital and the other close to certain schools and places of work. This method makes comparisons of such houses with other houses much easier.

In one of the implementation options, this method calculates the travel time PathDurations for clusters of houses along a certain number of routes to and from the place of work

PathDurations(/w/7i) = (Ji.i, ..., di, _m ),

PathDurationsf/W/fy) = (d _q ,i, ..., d _q ^.

After that, this method applies the generalized Deriver function, which does not work coordinate-wise, as in Section 6.3, but simultaneously for all q-m values of travel time and gives a vector of one or a set of numbers. In other words, the generic function looks like this:

Denver: R ^{? t} R<

for some y.

8. Search or compare.

In one implementation, the Deriver function is some kind of algorithm, such as a randomized algorithm, that takes some input (for example, travel routes to and from work, shortest travel times, home, or a condition specified by a user query) and produces some result (for example, the top list of houses that meet the user condition, with the shortest travel time, which also meets the user condition, sorted by the shortest travel time) [109].

9. Options.

People with basic technical knowledge will be well aware of multiple modifications and implementations without deviating from the general structure and essence of the implementation of the invention. Here are a few examples to illustrate.

9.1. Movement expansion.

In one implementation, this method first calculates the shortest time incompletely

- 14 042786 th move, and then expands (extends) it to the selected clusters of houses. There is no additional processing and storage to reduce storage and processing time due to fewer house clusters in vectors vi and v'i.

The method determines the connecting points (connectors) of houses, which are some elements of the transport system. In one implementation, house tie points are house clusters or stop clusters, which may be different from the clusters described in section 4.1. The method then precalculates and stores in the database the shortest travel time from the stop clusters to the house clusters using implementations similar to those described in section 4 of [112].

Upon receipt of a request, this method calculates the shortest travel time from the place of work W contained in the request to the selected clusters of houses. For this purpose, this method determines stop clusters near work W and extracts pre-calculated shortest travel times from nearest stop clusters to house tie points to obtain the shortest travel time between work W and house tie points, as described in Section 5. In one implementation, this calculation uses vector operations similar to those described in Sections 5.2 and 5.3. After that, these values of the shortest travel time are expanded beyond the connecting points of houses, obtaining the values of the shortest travel time between the place of work W and the selected clusters of houses. This can be done by simply finding, for each house cluster, the minimum extended move (which may contain more than just walkable parcels) whose route passes through some house tie point near the house cluster, for example, within 2000 m, and in some cases finding the direct shortest route between the workplace W and the cluster of houses (similar to Sections 5.2 and 5.3). In one embodiment, in overlap zones, this method uses both house tie points and vectors vi and v'i.

The quality of displacement extrapolation is proportional to the total number of house tie points, and also proportional to the number of house tie points near any selected cluster of houses. In one implementation, the expansion is used in only a few parts of the urban agglomeration, when the two quantities are likely to be small. In one implementation, this method uses the execution overhead function for the following purposes:

(1) determination of connecting points of houses;

(2) choice of house clusters; and (3) determining a subset of the nearest house tie points for each of the selected house clusters.

9.2. Moving along the route to the place of work and back by car.

In one implementation, the authors calculated the travel time on the route to and from work by car rather than by public transport. This is done by making minor modifications to the previous paragraphs.

In preprocessing the transport system for houses in Section 4, instead of using GT as the public transport system graph, let's take GT as the car traffic graph. The traffic pattern graph for a car can be obtained, for example, from known technical solutions. Such a graph may have vertices representing geographic locations on roads and edges representing vehicle movement or vehicle turning; edges can contain data about the time of movement at different times of the day, for example, during peak hours.

Let's expand GT. For each house cluster s, add vertices

HOMECLUSTER SOURCEs and

HOME CL USTER TARGET s.

Connect each cluster of houses to any roads that are within a threshold distance, such as 100 m, by adding a vertex

CONNECTOR r, for at least one r. In one implementation, the vertex denotes the shortest-distance projection of the location of the cluster of houses onto the road, which is within the threshold distance; the road can be inside the car park assigned to the cluster of houses. This vertex is connected to two vertices in the cluster of houses by edges labeled Zero and weighted to 0. The vertex is also connected to the vertices that represent the endpoints of the road segment. Instead of adding clusters of stops, which are not needed since GT does not model any metro stations or bus stops now, let's add vertices

REPRESENTA TIVESOURCEs' and

REPRESENTA TIVE TARGET J for array s' and t'; vertex data represents locations that are frequently encountered

- 15 042786 often occur on the shortest routes; arrangements can be obtained, for example, from known technical solutions. These vertices may represent clusters. These vertices are appropriately connected to other vertices using edges [117].

The authors use the extended GT model to calculate the shortest travel time for graph routes from each

REPRESENTA TIVESOURCEs’ before everyone

HOME CL USTER TARGET s, and from each

HOMECLUSTER SOURCEs up to each

REPRESENTA TIVE TARGETt’, implementations similar to those described in Section 4.1 can be used. These travel times will be stored as a vector vi and v'i as described in section 4.2.

When calculating the travel time along the route to and from the place of work, the authors used the movement by car instead of passing the pedestrian sections, as in section 5.

For the initial part of the move, we make the following modifications compared to section 5.2. Instead of walk(Hj^W ₁ ) we use the driving time from the cluster of houses Hj to W _b obtained, for example, from known technical solutions; in one implementation, we instead set such time as infinity if the distance between Hj and W ₁ exceeds a threshold value. Set A is a set of vertices

REPRESENTA TIVE TARGETJ' located within the threshold distance from W1. For each vertex s _i GA, the authors calculated the travel time by car from si to W1, using, for example, well-known technical solutions. Then the corresponding modifications were applied in equation 1 [120].

For the final part of the movement, we will make the same modifications, but now in section 5.3. Instead of walk(Wk^Hj), we use the driving time from W _k to the cluster of houses Hj, obtained, for example, from known technical solutions; in one implementation, we instead set such time as infinity if the distance between W _k and Hj exceeds a threshold value. Set B is a set of vertices

REPRESENTA TIVESOURCE s' located within the threshold distance from Wk. For each vertex sieb we calculate the driving time from W _k to s _i , using, for example, well-known technical solutions. Then we apply these modifications in equation 2 [121].

We use other implementations mentioned in section 5. For example, you can calculate the travel time by car along a geodesic line.

One can simply extend the calculation structure from section 6 to be able to limit the modes of transport used on each route to and from the place of work. As a result, you can determine, for example, the travel time along the route to and from work for each home of a family in which one of the parents travels to work located in geo1 by car five times a week, and the other parent travels to work in geo2 by public transport three times a week.

You can extend the comparison scheme in Section 7 in a similar way. As a result, you can, for example, find a new home from which the client will drive and compare with the current travel time by public transport. The result obtained by this method can be used as a motive for buying a car due to greater convenience when moving.

9.3. Moving using other modes of transport.

In one implementation, this method uses routes to and from the place of work with other modes of transport, for example, only on foot; only by bike; only by express bus and on foot; only by metro and on foot; only by express bus, metro and on foot; only in shared cars and on foot; water transport; on airplanes; etc. We simply use modifications similar to those described in Section 9.2. In one embodiment, the method identifies other homes and other means of transportation, makes recommendations to the user, and explains the benefit over the current home and current means of transportation.

The shortest arm of a graph on a given graph can be calculated without knowing the geographic locations of the different vertices of the graph. So, in one of the implementation options, this method uses a transport system, the various elements (elements) of which are not tied to a geographical location.

No need to physically move objects through the transport system. For this method, it is only necessary to be able to determine the route or lengths of routes between elements of the transport system. Thus, a computer network through which data moves is an example of a transport system, which includes the following transport elements: cables / lines (similar to roads)

- 16 042786 and network nodes/switches (similar to stops/turns). Anyone with basic technical knowledge can give many examples of transportation systems [127].

9.4. Conditions on routes of movement.

You can easily implement different filtering conditions for the travel paths. For example, one can construct a graph G that does not have transfers between any subway lines, but has walking distances between clusters of houses and clusters of stops. Together with modifications similar to those described in Section 9.2, this method will search or compare houses where the client will comfortably get from home to work (both home and work will need to be within walking distance of metro stations on the same line). Similarly, one can build G and change the algorithms for calculating the shortest arm of the graph to limit the graph arm to at most one transfer, either from the metro to the bus or from the bus to the metro, or a transfer at a certain time interval, or the type of route most often used by customers. This method provides other options for setting the travel route filter that anyone with basic technical knowledge can imagine.

9.5. Conditions at home.

In one implementation, this method obtains a filter condition for different characteristics of houses, searches for or compares houses whose characteristics match the condition. Characteristics can be the following: type (for example, a detached house or apartment in a high-rise), form of residence (for example, with a purchase or lease), price, real estate agency commission, taxes, maximum mortgage payment amount, number of rooms or bathrooms, area / size at home, the exit of windows to the cardinal points, the floor number in the house, the number of floors in the building or the standard amount of monthly utility bills. This method simply stores a list of characteristics for each house and, depending on the condition, determines the houses whose characteristics match the condition. The travel time for these matched houses can be obtained from the travel time for clusters of houses. This method provides other options for installing a house filter that anyone with basic technical knowledge can imagine.

9.6. Metasearch or comparison.

In one embodiment, the method searches or compares houses based on a combination of previous search and compare requests and their responses. This can be thought of as a meta method (a method that uses itself). It is useful, for example, to calculate a value that reflects the development potential of new properties.

Let us describe one of the options for implementing the metamethod. We got a certain number of routes to the place of work and back path1, ..., pathu. In one implementation, routes to and from work are taken from the history of using a computer service for finding and comparing houses, each route to and from work can be specified by different users of the service. For each route to and from work, pathk calculate the travel time for all clusters of houses PathDurations(path _k ) according to section 5. Then we apply an aggregator that will process the travel time values. In one of the implementation options for each route to the place of work and back path _k we get a vector of weight values w _k . In one implementation, each weight represents the probability that the user will select a particular house in the corresponding cluster of houses, which may be dependent on the property or travel path condition specified by the user query. Then we calculate the aggregates coordinate-wise, as shown in the following formula ^and - / w _k - PathDurations(pat / i _k ) and Z - । k=1 j-th unit is the weighted average travel time for the cluster of houses Hj. In one implementation, the j-th aggregate denotes the normalized contribution of the cluster of houses to the total travel time throughout the urban agglomeration; in a sense, it puts the cluster of houses in a central position relative to the urban agglomeration. Since this method quickly calculates PathDurations(path _k ), you can quickly calculate aggregates. This allows you to quickly calculate the demand for each property in terms of transport convenience [131].

People with basic technical knowledge can easily imagine many other ways to implement the metamethod. In other implementations, the routes to and from the place of work are based on the geographic locations of homes and places of work. In other implementations, the weights are set to non-zero for some set of house clusters with the shortest travel time, and zero for other clusters. In other implementations, the data scientist evaluates hypothetical scenarios; because thanks to the advantages of this method, this can be done quickly. In other implementations, the aggregator is an arbitrary algorithm, such as an algorithm that calculates variance, quantiles, cumulative distribution function, or probability of exceeding thresholds.

- 17 042786

9.7. A route to and from work with two or more houses.

In one implementation, the route to and from work includes (involves) any two or more houses. This is useful, for example, when searching and comparing houses for two or more families at once.

In one embodiment, H1 and H2 are two clusters of houses. It is possible to calculate the travel time for some route from the place of work and back H ₁ +path+H2, which starts at H1 but ends at H2, which may be different from H _b Just use j corresponding to H1 in equation 1, but in Equation 2 uses j corresponding to H2.

In one implementation, we precalculate both vectors (a1, ..., am) and (b1, ..., bm), and then find the travel time for two arbitrary house clusters Hi and Hj by simply adding the value of the coordinate (a1 , ..., am) corresponding to Hi to the coordinate value (b1, ..., b _m ) corresponding to Hj, plus the travel time along the intermediate part of the route (not tied to either Hj or Hj). Note that the travel time for any pair of house clusters, one of the m2 pairs, can be found from the time constant O(l) using only the vector space O(m). This is due to the additive structure of travel time and the fact that the route acts as a separator between any two clusters of houses.

In one embodiment, the set of house clusters allowed for H1 may be different from the set of house clusters allowed for H2. For example, a custom condition might constrain H1 to be in the east side of the city and H ₂ to be in the west side of the city. In this case, you can use a vector (b1, ..., bm) with length m' different from m.

More generally, this method calculates the travel time for some sequence of k>2 clusters of houses H ₁ ^path ₁ ^H ₂ ^path ₂ ^...^path _k . ₁ ^H _k . Using a preliminary calculation, this can be done in O(k) time and O(mk) space.

In one implementation, the route to and from work includes direct travel between clusters of houses, Hx+H _y , as in this example route to and from work: H ₁ ^path ₁ ^H _{x ^} H _y ^path ₂ ^H ₂ . In this example, this method divides the calculation into three parts:

(1) calculation of travel time H ₁ ^path ₁ ^Н _x ;

(2) calculation of travel time Hx+H _y ; and (3) calculating the travel time H _Y ^path ₂ ^H ₂ .

Parts (1) and (3) can be performed in the manner described above in this section 9.7. Part (2) can be carried out in a similar way if, in theory, either H _x or H _y is taken as the place of work. For example, using the vectors v'i in the coordinate corresponding to H _x , we get the travel time from the cluster of houses H _x to each cluster of stops; they can be extracted as a column from pre-computed vectors v'i, l<i<n. Then expand from each cluster of stops within the threshold distance from H _y to obtain a full travel to H _y similarly to section 5.2; see example in FIG. 8 and Equation 1. Thanks to the preliminary calculation by this method, (3) can be performed in time in proportion to the number of stop clusters within the threshold distance. In other implementations, since the house clusters are known in advance, we pre-calculate the travel time between each pair of house clusters, and then simply take the travel time as an O(l) time constant. A similar division naturally applies to any route to and from work that contains one or more direct transfers between clusters of houses.

9.8. Space exploration.

This method represents high quality exploration algorithms. Let's consider a situation when the client moves along a certain route to the place of work and back H ₁ +path+H2 with some cost; the cost function depends on the two houses H1 and H2. The client is looking for H1 and H2 houses to minimize this cost. This is useful, for example, when a family wants to change jobs (H1 and H2) of both parents at the same time, while minimizing the total travel time from the location of the current home (within the route) of the family; this is the well-known two-body problem.

One of the options for implementing space exploration is the gradient descent algorithm. The cost function can be a differentiable function; for example, given a fixed route, the function takes two houses H1 and H2 as input and returns as a result the distance between two houses H ₁ and H ₂ multiplied by the travel time along the route to and from work H ₁ +path+H2 (this function can be appropriately extended beyond the discrete domain of pairs of houses, for example, by the geographical location of houses and extrapolation). At a given step of the gradient descent algorithm, the algorithm calculates the gradient of the cost function given the pair of houses, and then selects the pair of houses in the direction of the gradient to perform the next step of the algorithm. The gradient can be calculated from the values of the cost function, for example, using a two-point formula (two-point formula), which requires two values. In one implementation, the result of the gradient descent algorithm is that pair of houses where the gradient has enough

- 18 042786 low criterion (norm) [140].

In one of the implementation options, we preliminarily calculate the vectors (a1, ..., am) and (b1, ..., b _m ) placed in the vector space O(m), and at each stage of this method we calculate the gradient by the constant O( l) time. Thus, the gradient descent algorithm can often speed things up.

In one implementation, we do not precalculate (a1, ..., am) and (bi, ..., b _m ), but instead obtain the necessary values from Equation 1 and Equation 2 when required. This approach can be used if the number of houses is so large that a preliminary calculation of (a1, ..., am) or (b1, ..., b _m ) is not practical.

In one embodiment, the space exploration algorithm may have restrictions on houses. For example, if a round-trip route to one house is required, the constraint would be H ₁ =H ₂ . You can restrict the geographic region allowed for H1 or allowed for H2.

In one implementation, the space exploration algorithm uses a route to and from work, including only one home: H ₁ ypath or pathyl 11 In other implementations, the space exploration algorithm uses a route to and from work, including two or more homes, as described in section 9.7.

In one implementation, the cost function depends on homes and places of work. For example, such a cost function may be used if the client is seeking to minimize the time-to-money cost ratio. In one implementation, the cost function is the travel time between H and W, plus the monetary cost of renting H, minus the wages paid on W, with possible weights that would indicate the relative importance of these components. In one implementation, due to the advantages of this method, gradient descent can be effectively used to find homes and jobs for such a cost function.

10. General case.

In one embodiment, the words home and work have an arbitrary semantic meaning. For example, consider a situation where a client is looking for a job that is close to their current home. The client does not want to move to another house, but simply wants to find a job closer to the current home. In this case, you can simply apply this method. Given a number of points throughout the urban agglomeration in which people work (for example, various institutions, enterprises, etc.), this method calculates the travel time between each cluster of jobs and each cluster of stops. Thus, this method can be considered a tool for searching or comparing jobs along the route to the place of work and back. In one embodiment, the method searches or compares jobs by the user's occupation or salary level, as well as travel time from the user's current home. As another example, consider a company that wants to move its head office to a new location. This method can be used to calculate the total travel time of the company for each new head office location throughout the metropolitan area. In this way, the company can determine how the new location will affect the routes of its employees to and from work. A new location can be chosen, for example, to (1) reduce travel time to and from work under the most adverse conditions; and (2) the average travel time to and from work was short, thus meeting the challenges for each employee and society as a whole.

This description says a lot about travel time as the main goal of a search or comparison. However, this method can be based on any other goals, such as the monetary value of the movement; distance in meters; certain characteristics or attributes of travel routes, such as the number of transfers or the length of walking distances; or characteristics of houses, such as price, size, or type. In one implementation, this is simply solved by building the corresponding graphs and setting the weight values of the edges. Different goals can be combined when searching with multi-objective optimization based on multi-dimensional cost, for example, when searching for a house whose location minimizes travel time, which is reflected in the financial costs of moving [147].

In the general case, this method uses arbitrary points S1, ..., S _m (the authors called places (site) houses in the sections above) and arbitrary places P1, ..., P _k (places (place) the authors called places of work in the sections above), and this method searches or compares points S1, ..., S _m by routes or route lengths (in the sections above, routes (route) was called the description of the movement, and the length of the route (route length) was called the distance of the movement) that start or terminate at some points or pass through some places, defined by arbitrary route specifications (route specification was the route to and from work in the sections above), including points and places. Any of the options described in clause 9 can be used for searching or comparing. Thus, this method can return routes or route lengths, or a representation of them, as a response. information, calculations

- 19 042786 obtained in one of the embodiments of the method, can be used recursively (recursively) as input for one or another embodiment of the method [148].

11. Computer system.

One of the embodiments of the invention is a computer system (computer system), which searches or compares real estate objects along the routes to and from the place of work. The authors have illustrated an embodiment of the computer system in FIG. eleven.

In this description, the authors use the term module (module). As known in the art, this term refers to a computer (sub)system that performs a specific functionality. This breakdown of the computer system into separate modules is presented as an option and is not mandatory. People with basic technical knowledge will note that the system can be modularized in a different way without violating the essence of the invention.

In one implementation, each movement along any route to the place of work and back contains the time of departure.

One module (1101) of the system reads data about the transport system from the data source (1102) and builds graph G. When building the graph, the module takes data about houses from the data source about real estate (1103), and from another data source (1104) takes the shortest walking areas between and near clusters of houses and clusters of stops. Column G contains data on the schedule of transport routes. The module produces a graph without vertices

HOME CLUSTER SOURCE s (1105) and also produces a graph without vertices

HOME CL USTER TARGET s but with inverted ribs (1106). The module also builds a data structure with nearest neighbor records (1107) to be able to find stops within a threshold distance from any geographic location, and precalculates shortest walking distances near house clusters and stop clusters (1108).

Simultaneously another module (1109) of the system reads two graphs and calculates the shortest arm of the graph. In one implementation, the module scans time slots every 5 minutes during the day. For each departure time, the module builds one table (1110) containing the shortest travel time from stop clusters to home clusters using (1105) and another table (1111) containing the shortest travel time from home clusters to stop clusters using (1106). In one implementation, each travel time, rounded to the nearest minute, is stored as a uint8 data type in the C++ programming language, reserving the maximum value of 255 as an indication of an unknown or very long travel time. In one implementation, tables are laid out (laid out) on HDDs in rows (row-major order). In one implementation, the system uses a cache hierarchy using HDDs, SSDs, and RAM. In one implementation, the tables or portions thereof are compressed using a compression algorithm such as delta compression. According to the authors' observations, for any pair from a cluster of houses and a cluster of stops, the travel time is often the same in certain time periods. This similarity is also often true in the neighboring environment of the couple. In one implementation, we select the sequence h1, ..., h _m of house clusters so that any hi and h _i+1 that are adjacent (adjacent) in the sequence are with high probability the nearest clusters of houses, and we select the sequence s1, . .., s _n stop clusters so that any si and s _i+1 that are adjacent in the sequence are, with high probability, the nearest stop clusters [153].

Modules (1101) and (1109) operate continuously. As a result, the system ensures that the travel time data is up-to-date, taking into account a specific departure time.

In parallel, the travel time module (1112) calculates PathDurations. Having a route to and from the place of work, as well as the time of departure, the module calls (1113) for the corresponding values of PathDurations, which have already been pre-calculated. Missing values are calculated from the starting position: the module calls the navigation data source (1114) to calculate the PathNonHomeDuration value for the portion of the route to and from work that does not include any homes. The module also calculates the travel time PathFromHomeDurations and PathToHomeDurations including homes by invoking nearest stop (1107), walking distance (1108), and travel time from home (1110 and 1111) vectors at the corresponding departure time.

In parallel, the query processing module (1115) searches or compares properties. Any request (1116) contains routes to and from work, including geographic locations on routes to and from work, and departure time, as well as the Deriver function. Upon receiving a request from the user, the module extracts the PathDurations from the travel time module (1112), applies the Deriver function, and returns information to the user expressing the result of the Deriver function (1117).

Aspects of the invention may be embodied in the form of a device, software, or

- 20 042786 hardware and software complex. Steps in the invention, such as circuit blocks, may be executed out of order, partially in parallel, or taken from the cache, depending on the functionality or optimization. Aspects of the invention may be implemented in a serial system or a parallel/distributed system in which each component contains a particular aspect; it is possible to provide for redundancy in other components, and communication between components can be implemented, for example, via any kind of network. The invention is not described with reference to any particular programming language. A computer program that performs operations on aspects of the invention may be written in any programming language, such as C++, Java, or JavaScript. Any program may run on any hardware platform, such as a central processing unit (CPU) or graphics processing unit (GPU), and associated storage devices or media. The program may execute aspects of the invention on one or more software platforms, including, but not limited to, smartphones running Android or iOS operating systems, or Internet browsers such as Firefox, Chrome, Internet Explorer, or Safari.

12. Computer service.

One of the options for implementing the invention is a computer service (computer service) for searching or comparing real estate objects along the routes to and from the place of work. The service is provided to users through the user device, for example, in the form of an application on a smartphone or a website on the Internet. It is obvious to any person with basic technical knowledge that the invention is not limited to use only on the listed devices. It is also obvious that the representation of the service in these diagrams can be changed (for example, by changing the layout, dimensions, colors, shape, adding or removing components) without violating the essence of the invention.

In one embodiment, the service is accessed through an application on a smartphone. See fig. 12 for illustration. The user enters a query. In one implementation, the request includes the desired properties of the property (1201), such as 3 rooms, multi-storey knowledge, upper floors;

routes to and from work (1202, 1203, Towsend or Jericho High, 1204), departure time (1205, 1206) and frequency of travel for each route (1207, 1208); and geographic location of the user's current home (1209).

In response, the service returns information about the travel time. For example, the service renders geographic locations of real estate objects that match a user query (1210). The service shows the dependence of travel time on the location of objects in comparison with the current home. The service shows brief information (summary) about the relevant property, such as its price. Properties can be stacked on a 2D map so that properties with shorter travel times are on the top layer and properties with longer travel times are on the bottom layer. If the number of objects is such that their normal display on the map is difficult, then the service can group the properties and display clusters, the size of which correlates with the number of properties in the cluster. The cluster can display brief information, for example, about the number, typical characteristics of real estate objects in the cluster [160].

In one implementation, the service shows properties with the shortest travel time. Brief information about real estate objects is also displayed (1211). Properties can be sorted by travel time.

In one implementation, the service displays a heatmap, on which the travel time from each area of the urban agglomeration is highlighted in color, for example, the minimum time for the area, as can be seen in the illustration of Fig. 1. The intensity map can show the difference in travel time for some homes and travel time for the user's current home. In one implementation, the intensity map shows only those properties that correspond to the desired user characteristics of the property [162].

In one implementation, the service displays a histogram of travel time (1212). The histogram contains travel time on one axis, and on the other axis, the proportion of properties whose location provides the corresponding travel time. In one implementation, the histogram only shows properties that match the user's desired property characteristics. In one embodiment, the user can hover over a portion of the histogram (1213) and the service will display the results of the travel time for that portion. In one implementation, this method uses another type of graph, such as a pie chart (pie chart) [163].

In one embodiment, the user may restrict travel routes, such as by limiting total walking time, number of transfers, etc., such as using range sliders (1214).

In one implementation, the service displays summary information about the travel route for the property.

- 21 042786

In one implementation, the service returns at least one of the following to the user:

(a) geographic location: a place or point displayed on a map;

(b) departure time or arrival time for: a place or point;

(c) brief information about the point; summary information may include at least one of the following: point name or address, point price, or point size;

(d) brief information about the points that form a cluster of nearest points;

(e) an image of a cluster of nearest points, an image size correlating with the number of points in the cluster of nearest points;

(f) location of points by z-index priority (z-index order) based on route length; shorter routes should be on the top layer of the map;

(g) route information and route length; information may include at least one of the following:

(i) route length, time, cost, speed or waiting time;

(ii) the name of the transport route, road, footpath, stop, turning point or transfer station between public transport routes; or (iii) geographic location in terms of cost, speed, waiting time, transportation route, highway, footway, stop, turning point or interchange station between public transport routes;

(h) histogram of route length through points; or a map of the intensity of route lengths through the points depicted on the map;

(i) minimum route length; histogram of the minimum route length through points; or an intensity map of the minimum length of the route through the points shown on the map;

(j) weighted route length; histogram of weighted route length through points; or an intensity map of the weighted route lengths through the points depicted on the map;

(k) differentiated route length; histogram of differentiated route length through points; or an intensity map of differentiated route lengths through the points depicted on the map;

(l) a picture of the result of applying the Deriver function;

(m) the point with the shortest route length through the points under the restriction on the monetary cost of movement;

(n) any of (a) through (m) above is subject to a condition specified by the user; or (o) a rating of points from a set of corresponding points, routes, and route lengths that meet a given condition, sorted by route length.

13. Note on the claims.

Those with basic technical knowledge should note that many modifications can be made, as well as substitutions for highly related equivalents, without violating the spirit of the present invention. In addition, the principles of the invention can be adapted to a particular situation without violating its essence. Thus, despite the disclosure of the mentioned embodiments of the invention, the invention should not be limited only to these embodiments. On the contrary, the invention will provide for all embodiments contemplated by the claims set forth in the appendix.

14. Glossary.

The authors have included a glossary of individual expressions found in the claims, as well as references to the specification. The links are not exhaustive; there are other links. The list of expressions is compiled in the order of the first mention of these expressions in the text of the claims.

The following expressions are also used in the claims, the meaning of which is explained.

1) The expression at least one A (at least one A) is equivalent to #A>1, where #A is the number A.

2) The expression one or more A (one or more A) is equivalent to #A>1, where #A is the number A.

3) The expression plurality of As (set A) is equivalent to #A>2, where #A is the number A.

4) The expression at least two As (at least two A) is equivalent to #A>2, where #A is the number A.

5) The expression one of A, or B (one of A or B) is equivalent to #A+#B=1, where #A is the number A and #B is the number B.

6) The expression at least one of A, or B (at least one of A or B) is equivalent to

- 22 042786 #A+#B>1, where #A is the number A and #B is the number B.

7) The expression at least one B or C (at least one B or C) is equivalent to at least one A, although each A is (B or C) (at least one A, where each A is (B or C) ).

expression link to usage example way (method) item[003] search or compare (search or compare) item[002] race (site) paragraph[148] route or route length items [013] , [127] place (place) paragraph[148] gransport system (transport system) item[022] representative (representative) items [022] , [117] storage item[022] database item[022] precomputed Section 4 movement description (description of travel) item[020] receiving item[003] request (request) item[022] starting place (start place) Section 5.2 end place (end place) Section 5.3 calculation (computing) item[089] nearest representative items [068] , [120] , [121] length of travel item[020]

- 23 042786

threshold value item[035] retrieving item[022] remote point (not nearby site) item[068] answer (responding) item[003] information item[003] designation (representation) paragraph[148] real estate object / end point of the route to the place of work and back (real estate property / commute destination) item[002] departure time / arrival deadline (departure time /arrival deadline) items [066] , [090] place Pi, start place Pi, end place Pk (place Pi, start place Pi, end place Pk) Definition 1 first point, last point (first site, last site) Section 9.7 includes (involve) Section 9.7 site-place route or route length item[091] cluster point / cluster representative (cluster site / cluster representative) items [035] , [036] cluster tie point (site connector) paragraph[112] compression (compression) paragraph[153] manipulation function (manipulation function) item[093] area item[092]

- 24 042786

(zone) transport elements paragraph[127] segment length (segment length) item[033] graph / graph vertexes (graph /graph vertexes) item[033] transport element vertexes Section 9.3 site vertex / representative vertex paragraph[117] graph edge item [033] graph edge source vertex / graph edge target vertex / graph edge weight item[033] graph arm or graph path length item[033] time item[042] algorithm (algorithms) item[033] inverted (reversed) item[040] coordinate item[056] vector v, value v[i] (vector v, value v/z7) item[056] vector ν', value v'[i] (vector ν', value ν'[if) item[058] placement (laying out) paragraph[153] list / hash table items [062] , [063]

- 25 042786

(list/hashmap) weight value w, (weight w _; ) item[059] lower bound Ibi, upper bound ub _t , scaling factor sf, (lower bound Ibi, upper bound up, scaling factor sf) item[060] operation "+", operation "min" (+ operation, min operation) item[072] first math formula / second math formula (first mathematical formula /second mathematical formula) items [072] , [086] celite (partitions) item[075] route specification E items [028] , [148] deriver function paragraph[109] minimum route length Section 6.2 weights wi,..., w _q (weights it7,..., Wq) item[099] weighted route length Section 6.1 point S (site 0) paragraph[105] differential route length Section 7.1 condition (condition) Sections 9.4,9.5 filter installation Section [006], Sections 9.4, 9.5 aggregator (aggregator) paragraph [131] central position paragraph [131]

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Claims (3)

(centrality) cost function (cost function) paragraph[140] research algorithm (exploration algorithm) Section 9.8 differentiable function item[140] gradient descent (gradient descent) [140] multi-objective optimization / multi-dimensional cost paragraphs [050] , [147] computer system (computer system) Section And instrument (apparatus) Section 12 summary / display / display priority (summary / rendering / stacking) item[160] heatmap item[162] histogram item[163] rating (top list) paragraph[109] CLAIM 1. A method of searching or comparing at least one point using at least two descriptions of movement in the transport system between the specified at least one point and at least one place, while the specified method includes (a) receiving a request that includes the specified by at least one place; (b) computing said at least two movement descriptions that include (i) a description of movement in said transportation system between each of a plurality of different places included in said at least one place and a point included in said at least one point , but not included in the specified set of different places, or (ii) a description of the movement in the specified transportation system between each of the many different points included in the specified at least one point, and a place included in the specified at least one place, but not included in the specified set of different points; and (c) responding to said request with an inferred movement description derived from said at least two movement descriptions. 2. The method according to claim 1, characterized in that said derived motion description is calculated using steps including (a) calculating a minimum of a plurality of motion lengths included in said at least two motion descriptions; (b) calculating a weighted sum of a plurality of movement lengths included in said at least two movement descriptions using numerical weights further included in said query; or (c) calculating the difference between a first travel length having an end point that is a first point and a second travel length having an end point that is a second point, said two travel lengths being included in said at least two travel descriptions , wherein the specified two points are included in the specified set of different points, and wherein one of the two points is additionally included in the specified query. 3. The method according to claim 1, characterized in that the point included in the specified at least one point, or the place included in the specified at least one place, are -