KR20220126475A - Online graph matching methods with worst-case reassignment budgets - Google Patents

Abstract

The present embodiments provide an online graph matching method that proposes a criterion that restricts the number of reallocations that occur whenever an object is known little-by-little and enables to comply with an appointment for which has been decided to pair the vertex. The online graph matching method comprises: a step of receiving the information; a step of selecting one increase path; and a step of matching for which does not perform increased matching.

Description

ONLINE GRAPH MATCHING METHODS WITH WORST-CASE REASSIGNMENT BUDGETS}

The technical field to which the present invention pertains relates to an online graph matching method.

The content described in this section merely provides background information for the present embodiment and does not constitute the prior art.

"Graph matching" is the problem of finding pairs that, given a set of vertices, and of which two pairs of vertices are allowed to pair with each other as edges, make as many pairs as possible, but prevent any vertices from being paired more than once. say

One representative application is online advertisement allocation from the perspective of a portal site. When a user accesses a portal site, one (or a certain number of) advertisements can be displayed on the screen that the user sees, so each query can be viewed as a vertex. Advertisements that the portal has pre-ordered from advertisers can also be viewed as the apex. Advertisers may or may not want to display their advertisements, depending on what the search terms in the query are.

A particular query-advertisement pair may or may not be able to be matched. Given the information about these pairs, it is a graph matching problem to expose as many advertisements as possible in order to maximize the profit of the portal.

In addition, the so-called load balancing problem of allocating tasks to cloud servers can be viewed as a graph matching problem, and the problem of maximizing the sum of the "scores" of each pair rather than the number of pairs can also be considered.

An "online problem" is one that requires an output and a commitment to it before the input is fully known. For example, in the advertisement allocation problem described above, since it is impossible to make a user who enters a search term wait forever, the portal site must select an advertisement to be exposed in the current query without knowing which user will enter which search term in the future.

Korean Patent Publication No. 10-1747854 (2017.06.09.)

In online graph matching, when there is a limit (k) in the number of vertices that can be paired again whenever an entity defined as a vertex or edge arrives in online graph matching, it is possible to find an appropriate approximate solution while keeping the promise to pair the vertices. has the main purpose of

Other objects not specified in the present invention may be additionally considered within the scope that can be easily inferred from the following detailed description and effects thereof.

According to an aspect of this embodiment, in an online graph matching method by an online graph matching apparatus, receiving an object defined as a vertex or an edge, including the received object and satisfying a constraint selecting one incrementing path from among augmenting paths, and performing matching increments by inserting and subtracting edges along the incrementing path if there is the selected incrementing path, or not performing matching increments if there is no selected incrementing path It provides an online graph matching method including a matching step.

The constraint may be defined as that the length of the increase path is shorter than or equal to the limit budget (k)-1 for the number of reallocations.

In the step of selecting one incremental path, a shortest path may be selected or a most beneficial increasing path according to a weight may be selected.

When interpreting the constraint conditions, the constrained budget may be considered to be smaller than the actual budget.

In the selecting step, the increment path is limitedly selected, the previously paired vertices are paired with a new vertex in the matching step, and as a result, the unpaired vertex is paired with another vertex after repeating the operation, You can keep your promise to match the vertices.

Through the matching step, a solution to the maximum-cardinality online matching problem under vertex arrivals according to the reception of the vertices having a limited budget k for the number of reallocations is provided with the competition ratio expressed by k. can

Through the matching step, a solution to the maximum-cardinality online matching problem under edge arrivals according to the reception of the edge having a limited budget k for the number of reallocations is provided with the competition ratio expressed by k. can

Through the matching step, a solution with a specific competition ratio for the maximum-weight online bipartite left-perfect matching problem under vertex arrivals according to the reception of the vertices with a limited budget for the number of reallocations can provide

As described above, according to the embodiments of the present invention, for the online graph matching problem, it is possible to present a criterion for limiting the number of reassignments that occur whenever an entity is known little by little, and to keep the promise of pairing vertices. there is an effect

Even if effects not explicitly mentioned herein, the effects described in the following specification expected by the technical features of the present invention and their potential effects are treated as described in the specification of the present invention.

1 is a block diagram illustrating an online graph matching apparatus according to an embodiment of the present invention.
2 is a flowchart illustrating an online graph matching method according to another embodiment of the present invention.

Hereinafter, in the description of the present invention, when it is determined that the subject matter of the present invention may be unnecessarily obscured as it is obvious to those skilled in the art with respect to related known functions, the detailed description thereof will be omitted, and some embodiments of the present invention will be described. It will be described in detail with reference to exemplary drawings.

In the case of cloud server load balancing, for example, a promise to a vertex once "promised to be paired" must be kept, but two specific vertices may not necessarily be paired. A job in progress on one cloud server can be moved to another server. You can't do too many "reassignments" of remapping vertices at once, so if you can solve the online graph matching problem with a limit on the number of possible reallocations at a time, you can't do online graph matching where previously reallocations are not allowed. It will be possible to apply the new technology to various fields where matching has been applied.

According to this embodiment, matching of a bipartite graph (in the same case as the previous query-advertising assignment problem or cloud server load balancing problem, where there are two kinds of vertices and only different kinds are paired with each other), each edge has a score and the number is For a situation in which the score must be maximized, the vertices are known little by little, but the edges are known little by little, even if it is not an optimal solution (it is impossible to find an optimal solution because it is impossible to find an optimal solution before seeing all the inputs) provide a way This is accomplished by selecting a so-called augmenting path to be short, and repeating the operation of subtracting the edge included in the match and inserting the edge not included along the augmenting path.

1 is a block diagram illustrating an online graph matching apparatus according to an embodiment of the present invention.

The online graph matching apparatus 110 includes at least one processor 120 , a computer-readable storage medium 130 , and a communication bus 170 .

The processor 120 may control to operate as the online graph matching apparatus 110 . For example, the processor 120 may execute one or more programs stored in the computer-readable storage medium 130 . The one or more programs may include one or more computer-executable instructions, which, when executed by the processor 120 , configure the online graph matching apparatus 110 to perform operations according to the exemplary embodiment. can be

Computer-readable storage medium 130 is configured to store computer-executable instructions or program code, program data, and/or other suitable form of information. Computer-executable instructions or program code, program data, and/or other suitable form of information may also be provided via input/output interface 150 or communication interface 160 . The program 140 stored in the computer-readable storage medium 130 includes a set of instructions executable by the processor 120 . In one embodiment, computer-readable storage medium 130 includes memory (volatile memory, such as random access memory, non-volatile memory, or a suitable combination thereof), one or more magnetic disk storage devices, optical disk storage devices, flash It may be memory devices, other types of storage media accessed by the online graph matching apparatus 110 and capable of storing desired information, or a suitable combination thereof.

The communication bus 170 interconnects various other components of the online graph matching apparatus 110 , including the processor 120 and the computer readable storage medium 130 .

The online graph matching device 110 may also include one or more input/output interfaces 150 and one or more communication interfaces 160 that provide interfaces for one or more input/output devices. The input/output interface 150 and the communication interface 160 are connected to the communication bus 170 . The input/output device (not shown) may be connected to other components of the online graph matching device 110 through the input/output interface 150 .

The online graph matching device 110 selects an augmenting path limitedly, pairs previously paired vertices with new vertices, and repeats the operation of pairing lost vertices with other vertices as a result. Find a suitable approximation solution while keeping the promise of the vertices. It can provide a criterion to set a limit on the number of reallocations that occur whenever an object is known little by little, and it can keep the promise of vertices.

A bipartite graph refers to a graph in which the vertices at both ends of all existing edges belong to different groups when the vertices are divided into two groups.

Binary matching is a configuration in which each vertex is adjacent to at most one vertex in a bipartite graph. A vertex may be referred to as a node or the like, and an edge may be referred to as an edge or the like.

A path that starts from an edge not included in a given match, alternates between not included and included edge, and ends with an edge not included is called an incremental path. After selecting the increment path, by excluding the previously included edges and including the not included edges along the increment path, the number of edges of the existing matching can be increased by one. The incremental path can be found by BFS (Breadth First Search) or the like.

2 is a flowchart illustrating an online graph matching method according to another embodiment of the present invention. The online graph matching method may be performed by an online graph matching apparatus.

In step S20, information on an entity defined as a vertex or an edge is received. Objects are entered in a time series according to time stamps, rather than all inputs being entered at once.

In step S30, one augmenting path is selected from among augmenting paths that include the newly arrived entity and satisfy the constraint. In the step of selecting one increasing path ( S30 ), a shortest path may be selected or a path most beneficial according to a weight may be selected. If there is no incremental path that includes the newly arrived object and satisfies the constraint, the incremental path is not selected.

In step S40, if there is a selected incremental path, matching increment by inserting and subtracting edges along the increment path is performed, or if there is no selected increment path, a matching step of not performing matching increment is performed.

The constraint may be defined that the length of the incremental path is shorter than or equal to the constraint budget (k)-1 for the number of reallocations. If necessary, the constrained budget (k) can be considered smaller than the actual budget.

In the step of selecting the incremental path (S30) and the matching step (S40), an incremental path is limitedly selected, the previously paired vertices are paired with a new vertex, and as a result, the unpaired vertex is paired with another vertex. can do.

It may include a step (S10) of receiving partial information on the whole of the graph before the step (S20) of receiving the information on the object.

After the matching step (S40), it may include a step (S50) of checking whether there is an object to be further received. If there is an object to be further received, the step S20 of receiving information on the object is performed again.

경쟁비로 해를 제공할 수 있다. 경로를 선택하는 단계(S30)에서 가중치가 적용되지 않는 온라인 그래프 매칭 문제에 대해서 최단 증가 경로를 선택할 수 있다.For the maximum-cardinality online matching problem under vertex arrivals according to the reception of vertices having a limited budget k for the number of reallocations through the step S30 and the matching step S40 of selecting an incremental path expressed as k

Competitive costs can provide harm. In the step of selecting a path ( S30 ), the shortest increasing path may be selected for the online graph matching problem to which no weight is applied.

경쟁비로 해를 제공할 수 있다. 경로를 선택하는 단계(S30)에서 가중치가 적용되지 않는 온라인 그래프 매칭 문제에 대해서 최단 증가 경로를 선택할 수 있다.For the maximum-cardinality online matching problem under edge arrivals according to the reception of an edge having a limited budget k for the number of reallocations through the step S30 and the matching step S40 of selecting an incremental path expressed as k

Competitive costs can provide harm. In the step of selecting a path ( S30 ), the shortest increasing path may be selected for the online graph matching problem to which no weight is applied.

Maximum-weight online bipartite left-perfect matching problem according to the reception of vertices having a limited budget for the number of reallocations through the step S30 and the matching step S40 of selecting an incremental path under vertex arrivals) can provide a solution at a certain competitive rate. For example, the specific competition ratio may mean 1/2-competition ratio. In the step of selecting a path ( S30 ), it is possible to select a path that is most profitable for the weighted online graph matching problem. Even when k of the constraint condition exceeds 4 in the matching step ( S40 ), k may be regarded as 4 .

The online graph matching apparatus may be implemented in a logic circuit by hardware, firmware, software, or a combination thereof, or may be implemented using a general-purpose or special-purpose computer. The device may be implemented using a hardwired device, a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or the like. In addition, the device may be implemented as a system on chip (SoC) including one or more processors and controllers.

The online graph matching apparatus may be mounted in the form of software, hardware, or a combination thereof on a computing device or server provided with hardware elements. A computing device or server is all or part of a communication device such as a communication modem for performing communication with various devices or a wired/wireless communication network, a memory for storing data for executing a program, and a microprocessor for executing operations and commands by executing the program It can mean a variety of devices, including

Although it is described that each process is sequentially executed in FIG. 2, this is only illustratively described, and those skilled in the art change the order described in FIG. 2 without departing from the essential characteristics of the embodiment of the present invention. Alternatively, various modifications and variations may be applied by executing one or more processes in parallel or adding other processes.

The operations according to the present embodiments may be implemented in the form of program instructions that can be performed through various computer means and recorded in a computer-readable medium. Computer-readable medium represents any medium that participates in providing instructions to a processor for execution. Computer-readable media may include program instructions, data files, data structures, or a combination thereof. For example, there may be a magnetic medium, an optical recording medium, a memory, and the like. A computer program may be distributed over a networked computer system so that computer readable code is stored and executed in a distributed manner. Functional programs, codes, and code segments for implementing the present embodiment may be easily inferred by programmers in the technical field to which the present embodiment pertains.

The present embodiments are for explaining the technical idea of the present embodiment, and the scope of the technical idea of the present embodiment is not limited by these embodiments. The protection scope of this embodiment should be interpreted by the claims below, and all technical ideas within the scope equivalent thereto should be construed as being included in the scope of the present embodiment.

Claims (5)

In the online graph matching method by the online graph matching device,
Receiving information on an object defined as a vertex or an edge;
selecting one augmenting path from among augmenting paths that include the received entity and satisfy a constraint; and
and a matching step of performing matching increment by inserting and subtracting edges along the increment path if there is the selected increment path, or not performing matching increment if there is no selected increment path. According to claim 1,
The online graph matching method, characterized in that the constraint is defined as that the length of the increasing path is shorter than or equal to the limit budget (k)-1 for the number of reallocations. 3. The method of claim 2,
and the limited budget is considered to be smaller than the actual budget. 4. The method according to any one of claims 1 to 3,
The step of selecting one increasing path is an online graph matching method, characterized in that selecting the shortest path or selecting the most profitable increasing path according to a weight. 5. The method according to any one of claims 1 to 4,
(i) provide a solution with the competition ratio expressed by k for the maximum-cardinality online matching problem under vertex arrivals according to the reception of the vertices having a limited budget k for the number of reallocations, or
(ii) provide a solution with the competition ratio expressed by k for the maximum-cardinality online matching problem under edge arrivals according to the reception of the edge having a limited budget k for the number of reallocations, or
(iii) to provide a solution with a specific competition ratio to the maximum-weight online bipartite left-perfect matching problem under vertex arrivals according to the reception of the vertices with a limited budget for the number of reallocations Online graph matching method, characterized in that.

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