KR20080113953A - Method and system for finding nearest neighbors based on vboronoi diagram - Google Patents

Abstract

A nearest neighbor searching method and system based on the Voronoi diagram are provided to reduce the number of distance operation by not performing direct minimum distance calculation and not requiring distance update operation according to POI expansion. A nearest neighbor searching system based on the Voronoi diagram comprises a storage unit(350) which stores boundary minimum distance information, and a nearest query processing unit(370) processing a fixed number of nearest neighbor query and providing POI corresponding to the processed query result by using the boundary minimum distance information stored in the storage unit. The storage unit includes a cell minimum distance storage part for storing cell minimum distance information and a boundary minimum distance storage part for storing boundary minimum distance information.

Description

Near-point search method and system based on Voronoi diagram {METHOD AND SYSTEM FOR FINDING NEAREST NEIGHBORS BASED ON VBORONOI DIAGRAM}

1 is a diagram showing a state of spatial division for explaining the basic principle of the Voronoi diagram.

2 is a diagram illustrating an example of applying a Voronoi diagram to a road network.

3 is a diagram illustrating a configuration of a nearest-point search system based on a Voronoi diagram according to the present invention.

4 is a diagram illustrating the entire process of a minimum distance matrix generation algorithm between boundary points according to the present invention.

5 is a diagram for describing a process of generating a minimum distance matrix between boundary points.

6 is a diagram illustrating the entire process of a k-nearest point query processing algorithm based on a minimum distance matrix between boundary points according to the present invention.

7 shows a network Voronoi diagram based on the k-nearest query processing algorithm of the present invention.

8 is a diagram illustrating an interval distance calculation table according to the k-nearest point query processing algorithm of the present invention.

<Explanation of symbols for main parts of the drawings>

310: cell information storage unit 330: cell minimum distance storage unit

350: Minimum boundary line storage unit 370: Nearest query processing unit

The present invention relates to a nearest point search algorithm, and more particularly, to a nearest point search method and system for processing a k-nearest point query using a Voronoi diagram applied to a road network.

In general, a navigation system detects a current position of a moving object by receiving a phase propagation from a global positioning system (GPS) satellite that navigates the earth's atmosphere and calculates a radio wave reception distance from the satellite, and stores a storage medium containing map data. The current position of the moving object detected from the map data for the relevant region is displayed.

In addition, by calculating the driving direction by the driving distance determined by the driving distance detecting means such as the wheel rotation detecting sensor and the azimuth angle detecting means such as the geomagnetic sensor, the driving route from the starting position to the running position is displayed on the screen. can do.

Searching for near point of interest (POI) near a user in real time while moving is an essential function of a navigation system, and a fast search method is required to support this.

In geographic information system (GIS), location-based services (LBS) and telematics applications, a service that recommends a few POIs close to the current location, such as gas stations, restaurants and banks, is essential.

This neighbor POI search is possible by the nearest query processing method, and it uses an algorithm that stores the road network to process the nearest query and expands the network until it reaches the POI to find at a given query point to find the POI. . However, in order to reduce costs, an algorithm for processing nearest-neighbor queries using voronoi diagrams has been developed.

The Voronoi diagram refers to a method of dividing a space based on points spaced at the same distance from each vertex when there are many vertices in the space.

These voronoi-based network nearest neighbor algorithms (hereinafter referred to as 'VN3') based on these network Voronoi diagrams are used to search for k nearest neighbors (POIs) from any point on the road. It was developed for the nearest neighbor query.

In essence, VN3 applies the Voronoi diagram method to road networks, using network voronoi polygons to quickly calculate the first nearest object. In addition, the POIs may be extended using network Voronoi polygons adjacent to each other to calculate the nearest points from the second to the kth.

The k-nearest point search method based on the network Voronoi diagram is as follows.

First, the Voronoi diagram ensures that P1 is the nearest vertex of query point q when query point q exists in the cell of P1 as shown in FIG.

FIG. 2 applies the Voronoi diagram of FIG. 1 to a road network. When the Voronoi diagram is applied to the network, unlike the Voronoi diagram, Dijstra algorithm is used to find the distance between each Voronoi cell.

The network Voronoi diagram obtains a boundary line of each Voronoi cell and then generates a Voronoi diagram based on this.

When the network Voronoi diagram is generated, the distance from the vertex of the network to the boundary line, the distance from the boundary line to the boundary line, and the distance from the POI to the boundary line in each cell are calculated.

Then, the distance from the query point to the POI is calculated by summing the calculated distance values. Then, the minimum distance to each POI is inserted into a minimum heap to search for the POI having the shortest distance from the minimum heap, and set it as the next nearest neighbor.

However, the conventional k-nearest point search method calculates the distance from the query point (q) to the boundary point of the Voronoi cell including the POI and the distance calculation from the boundary point of the Voronoi cell when performing the nearest point query. As required, it takes time Θ (m + nlgn) (m: number of edges, n: number of nodes) to calculate the minimum distance to the POI. That is, if k POIs are found, it takes kΘ (m + nlgn) to calculate the distance.

Therefore, VN3 takes a lot of time to construct a network Voronoi polygon when the k value is increased or the data density is increased, and the computational complexity increases exponentially, resulting in a decrease in system performance.

In addition, the existing k-nearest point query search algorithm needs to calculate the distance between the boundary points due to the newly inserted boundary section while extending the POI at the query point q. . In addition, the minimum distance from the query point (q) to the boundary point should be updated with the newly inserted section.

That is, when the POI is extended in the existing k-nearest point query, the minimum distance between the boundary points occurs on the network, and this update is necessary, so each time the POI is extended, the repetition of the interval is repeated. There is a problem that needs to be done.

The present invention provides a k-nearest query processing algorithm that minimizes the time required to construct a network Voronoi polygon and minimizes k-nearest query computation.

In addition, the present invention maintains the minimum distance between the boundary points of the Voronoi cells from the point of view of the entire network, thereby minimizing the distance update problem and optimizing the k-nearest point query processing performance. Provide an algorithm.

According to another aspect of the present invention, there is provided a network including: a storage unit for storing boundary minimum distance information including a minimum distance matrix between boundary points of a Voronoi cell in an entire road network to which a Voronoi diagram is applied; And a neighboring query processing unit configured to provide a POI corresponding to the processed query result after processing a predetermined number of nearest neighbor queries using the boundary minimum distance information stored in the storage unit. It provides a closest point search system based on.

In addition, the present invention provides a method comprising: maintaining boundary minimum distance information including a minimum distance matrix between boundary points of a Voronoi cell in a whole road network to which a Voronoi diagram is applied; Searching for a predetermined number of nearest neighbors corresponding to an arbitrary query point using the boundary minimum distance information; And providing a POI corresponding to the searched nearest point of the query point, based on a Voronoi diagram.

According to the present invention, by maintaining the minimum distance between the boundary points of the Voronoi cells in the entire network through the storage medium, the distance update operation according to the regional distance extension can be omitted and the query processing time can be greatly shortened.

Hereinafter, with reference to the accompanying drawings will be described a near-point search system and the nearest point search method based on the Voronoi diagram according to the present invention.

First, with reference to Figure 3 will be described in detail the configuration of the nearest-contact search system based on the Voronoi diagram of the present invention.

The closest point search system of the present invention is intended to be applied to a navigation terminal having a GPS receiver for receiving position signals from at least three GPS satellites.

The navigation terminal receives a position signal through a GPS receiver, calculates the position of the moving object, informs the user of the current position based on the calculated position of the moving object (Location), and calculates an optimal route to a desired destination (Routing). According to the route, the user is guided while providing various information related to the route.

In addition, the navigation terminal provides a function of searching for a nearest neighbor based on the current position of the moving object. By using this function, various navigation points (POIs) adjacent to the current position such as a gas station, a restaurant, a bank, etc. during the route movement are used. search for and provide it.

The present invention provides a nearest-contact query processing algorithm based on a boundary minimum distance matrix on a road network using a Voronoi diagram for a nearest-contact search function on a navigation terminal.

The system configuration for providing the nearest-contact query processing algorithm according to the present invention includes boundary minimum distance information including a minimum distance matrix between boundary points of the Voronoi cells in the entire road network to which the Voronoi diagram is applied, as shown in FIG. Storage unit for storing; And a nearest query processing unit 370 that processes a predetermined number of nearest point queries using the boundary minimum distance information stored in the storage unit and then provides a POI corresponding to the processed query result to the user.

The storage unit may include a cell information storage unit 310 for storing cell information including a boundary point of a Voronoi cell in the entire network, a minimum distance between a POI (point of interest) in the Voronoi cell and a node, Cell minimum distance storage unit 330 for storing the minimum cell distance information including the minimum distance between the POI and the boundary point, and boundary minimum distance storage unit for storing the boundary minimum distance information including the minimum distance matrix between the boundary points in the entire network And 350.

The storage unit may further include a map database for constructing map data for a nationwide map and route guidance data associated with the map data for guiding a route to a destination designated by a user.

The present invention includes a configuration in which cell information, cell minimum distance information, and borderline minimum distance information of the entire network are pre-calculated and maintained and provided through the storage unit for the nearest-contact query processing.

The nearest query processing unit 370 searches k nearest contact points based on the query points corresponding to the current location of the user by using the stored cell information, cell minimum distance information, and boundary minimum distance information. The closest contact is provided as POI information through the display device of the navigation terminal.

Therefore, the present invention does not require the calculation of the minimum distance between boundary points in the process of performing the nearest-contact query by constructing and maintaining boundary minimum distance information on the entire network in advance. This can solve the problem of distance update.

Hereinafter, a method of generating a minimum distance matrix between boundary points stored in the storage unit and a method of searching for the nearest point to a query point based on the boundary minimum distance matrix will be described in more detail.

FIG. 4 is a diagram illustrating the entire process of the algorithm for generating the minimum distance matrix between boundary points according to the present invention, and FIG. A diagram illustrating the process.

4, a method of generating a minimum distance matrix between boundary points will be described first.

After generating a Voronoi diagram applied to the road network, an arbitrary boundary point of the Voronoi cell is designated (S410), and another boundary point which is the object of distance calculation with the designated boundary point is designated (S420).

If two different boundary points are designated, at least one distance matrix is generated between the two designated boundary points, and an edge (road, road) including the two boundary points is searched on the road network (S430).

The minimum distance between nodes (intersection points) constituting the searched edge and the distance between the node and each boundary point are calculated (S440 to S460).

Here, it is determined whether there is a minimum distance matrix between nodes (intersection points) constituting the searched edge on the basis of the map data stored in the storage unit and the cell minimum distance information. Read the minimum distance between nodes in the matrix. On the other hand, if there is no minimum distance matrix between the nodes using the dijstra algorithm to calculate the minimum distance between the nodes.

After calculating the distance between two boundary points according to each distance matrix generated for the two boundary points using the calculated minimum distance between the nodes and the distance between the node and each boundary point, the distance between the boundary points is The distance matrix having the minimum distance among the calculated distance matrices is stored as the minimum distance matrix between the two boundary points (S470 to S490).

For example, as shown in FIG. 5, when two boundary points for which the minimum distance is to be calculated are designated b _i (1 ≦ _i ≦ n) and b _j (1 ≦ _j ≦ n), as shown in FIG. Four point distance matrices D _{1 , 1} , D _{1 , 2} , D ₂ , ₁ , D _{2 , 2} are possible between points.

At this time, the distance (D _{1 , 1} , D _{1 , 2} , D _{2 , 1} , D _{2 , 2} ) between two boundary points for each distance matrix is as follows.

D _{1 , 1} = Dist (n _{(i, 1)} , b _i ) + Dist (n _{(i, 1)} + n _{(j, 1)} ) + Dist (n _{(j, 1)} , b _j )

D _{1 , 2} = Dist (n _{(i, 1)} , b _i ) + Dist (n _{(i, 1)} + n _{(j, 2)} ) + Dist (n _{(j, 2)} , b _j )

D _{2 , 1} = Dist (n _{(i, 2)} , b _i ) + Dist (n _{(i, 2)} + n _{(j, 1)} ) + Dist (n _{(j, 1)} , b _j )

D _{2 , 2} = Dist (n _{(i, 2)} , b _i ) + Dist (n _{(i, 2)} + n _{(j, 2)} ) + Dist (n _{(j, 2)} , b _j )

Where i ≠ j, n _{(i, j)} (1≤i≤n, j = 1 | 2) is a node including two boundary points, and Dist (n _{(i, 1)} , b _i ), Dist (n _{(j, 1)} , b _j ) is the distance between the node and the boundary point for the first distance matrix, and Dist (n _{(i, 1)} + n _{(j, 1)} ) is the node for the first distance matrix Means the distance between.

When the distance calculation between the two boundary points for each distance matrix is completed, the distance matrix having the minimum distance value is set as the minimum distance matrix MinDist _{i , j} between the two boundary points.

By repeating the above steps (S410) to (S490), a minimum distance matrix between boundary points is set for all boundary points on the entire network (S500), and when the minimum distance matrix is completed for all boundary points, the boundary points between the boundary points are completed. The boundary minimum distance information including the minimum distance matrix is constructed in the storage unit.

In particular, when storing the minimum distance matrix between the boundary points in the storage unit, it is preferable to store the distance matrix between the boundary points in units so as to facilitate data access when performing the nearest-contact query.

The present invention performs the nearest-neighbor query processing algorithm using the minimum distance matrix between boundary points constructed in the storage unit.

Next, a method of searching for the nearest point by the nearest point query processing algorithm of the present invention will be described with reference to FIG.

When there is a query requesting the search for the nearest point in the process of moving the path designated by the user, the current position of the user is determined and the determined current position is used as the query point.

As shown in the figure, the Voronoi cell including the query point is searched on the road network and the POI of the found Voronoi cell is set as the first nearest point (S600).

Subsequently, the POI having the minimum distance with the query point is sequentially searched for the query point and the neighboring Voronoi cell, and set as the next nearest point.

Determining a distance (A) from the boundary point of the Voronoi cell including the query point to the query point (hereinafter referred to as 'first distance') to set the next nearest point, and the query point Determining a minimum distance (hereinafter referred to as 'second distance') B between a Voronoi cell and a boundary point of a neighboring Voronoi cell, and the neighboring point at the boundary point of the neighboring Voronoi cell A process of determining a minimum distance (hereinafter referred to as 'third distance') C to the POI of the Voronoi cell is sequentially performed.

First, in order to determine the first distance A, it is determined whether two nodes (intersection points) of an edge (road or road) including the query point include different Voronoi cells (S620). As a result of the determination, when two nodes of the edge including the query point exist in one Voronoi cell, the distance from the boundary point including the query point to the query point is calculated to be the first distance A. Set (S640).

On the other hand, when two nodes of the edge including the query point includes two Voronoi cells, the distance from the boundary point of the Voronoi cell including the query point to the respective nodes is calculated and the minimum distance among them In step S630, a distance having a distance is selected as the first distance A. FIG. That is, when the edge including the query point includes two Voronoi cells, the first distance A is determined by considering both Voronoi cells.

Here, when two nodes of the edge including the query point include two Voronoi cells, the first distance A may be defined as in Equation 1 below.

Dist (q, b _i ) = Min (Dist (q, n ₁ ) + Dist (n ₁ , b _i ), Dist (q, n ₂ ) + Dist (n ₂ , b _i ))

Where q is the query point, and b _i is the boundary point of the Voronoi cell containing the query point, and Dist (q, b _i ) is the distance from the boundary point of the Voronoi cell containing the query point to the query point, n ₁ , n ₂ : node containing the query point, Dist (q, n ₁ ), Dist (q, n ₂ ): distance from the query point to each node, Dist (n ₁ , b _i ), Dist (n ₂ , b _i ): distance from the boundary to each node)

Next, in order to determine the second distance B, first, the Voronoi cell including the query point and the neighboring Voronoi cell are searched based on the boundary minimum distance information stored in the storage unit (S650).

Subsequently, the minimum distance B between the boundary point of the neighboring Voronoi cell and the neighboring Voronoi cell is retrieved from the stored boundary minimum distance information (S660). It searches for the boundary point of the Voronoi cell including the query point in the minimum distance matrix between the boundary points stored in the storage unit, and the neighboring Voronoi having the minimum distance matrix and the boundary point of the Voronoi cell including the query point. To find the boundary of a cell. In addition, the second distance B is the minimum distance between the Voronoi cell including the query point corresponding to the minimum distance matrix and the boundary point of the neighboring Voronoi cell.

Finally, in order to determine the third distance C, cell minimum distance information corresponding to the neighboring Voronoi cell is retrieved from the cell minimum distance information stored in the storage unit. The minimum distance between the boundary point of the neighboring Voronoi cell and the POI point of the neighboring Voronoi cell is searched for from the found cell minimum distance information and set as the third distance C (S670).

When the determination of the first to third distances A, B, and C is completed through the above processes, the first to third distances A, B, and C are added together to add the query The minimum distance from the point to the POI of the neighboring Voronoi cell is calculated (S680).

The minimum distance from the query point to the POI of the neighboring Voronoi cells may be defined as in Equation 2.

MinDist _{q , p} = Min (Dist (q, b _i ) + Dist (bi, bj) + Dist (bj, p))

Where: q: query point, p: POI point, MinDist _{q , p} : minimum distance from query point to POI point of neighboring Voronoi cell, b _i : boundary point of Voronoi cell including query point, b _j : boundary point of neighboring Voronoi cell, Dist (q, b _i ): distance from the boundary point of Voronoi cell including query point to query point (first distance) (A), Dist (bi, bj ): Distance between the Voronoi cell containing the vaginal point and the boundary point of the neighboring Voronoi cell (second distance) (B), Dist (bj, p): To the boundary point and POI point of the neighboring Voronoi cell Distance (3rd street) (C)

Accordingly, when determining the first to third distances A, B, and C, distance values calculated in advance from cell minimum distance information or boundary minimum distance information stored in the storage unit are used. That is, since the present invention uses the minimum distance matrix between boundary points pre-calculated and stored at the time of performing the nearest-contact query, the minimum boundary distance can be retrieved from the storage without directly calculating the distance between the boundary points.

The POI of the neighboring Voronoi cell having the minimum distance through the minimum heap is inserted into the minimum heap by inserting the distance from the calculated query point to the POI of the neighboring Voronoi cell into the minimum heap. Set (S690).

Repeat the steps (S650) to (S690) until the number of POIs set as the nearest point reaches the predetermined number k, search for other neighboring Voronoi cells, and expand the POI to set the nearest point. Repeat.

FIG. 7 is a diagram showing an example of a network Voronoi diagram based on the k-nearest query processing algorithm of the present invention, and FIG. 8 is a diagram showing an interval distance calculation table for the network Voronoi diagram of FIG. .

7 and 8, a process of calculating the distance between the query point and the POI according to the nearest-contact query algorithm of the present invention will be described.

In the Voronoi diagram of FIG. 7, the order of nearest contact setting is P ₁ based on the query point (q). -> P ₃ -> P ₄ -> P ₂ Follow in order. Since P ₁ is the Voronoi cell containing the query point, it becomes the first nearest point and the interval calculation is performed twice. P ₃ is the second POI and the interval calculation is performed four times.

For a P _4, a minimum distance between P ₄ and P ₅ boundary points the circuit by building in the storage unit in advance without having to calculate the number of all cases passing the boundary point in the order from P ₄ to calculate the minimum distance to P ₅ Through the matrix, the minimum distance from the boundary point of P ₁ of the Voronoi cell including the query point to P ₅ can be known. That is, since there is no need to recalculate the minimum distance, P ₄ is composed of six interval calculations. In addition, in case of P ₂ , the minimum distance between the boundary points of the entire network is maintained without updating the minimum distance from the query point to the candidate set, so the update operation is not necessary due to the selection of P ₂ . Therefore, in the case of P _{2 in} the present invention, the number of calculations is zero.

The present invention reconstructs and updates the minimum distance due to POI extension by pre-establishing cell minimum distance information and borderline minimum distance information for a Voronoi cell on an entire network in a storage unit and using the same when performing a nearest point query. Can be omitted.

The closest point search method based on the Voronoi diagram according to the present invention can be implemented in the form of program instructions that can be executed by various computer means and recorded in a computer readable medium. The computer readable medium may include a program command, a data file, a data structure, etc. alone or in combination. Program instructions recorded on the media may be those specially designed and constructed for the purposes of the present invention, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, such as floppy disks. Magneto-optical media, and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

As described above, although the present invention has been described with reference to limited embodiments and drawings, the present invention is not limited to the above embodiments, and those skilled in the art to which the present invention pertains various modifications and variations from such descriptions. This is possible.

Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined not only by the claims below but also by the equivalents of the claims.

The closest point search method and the system based on the Voronoi diagram of the present invention pre-establish cell minimum distance information and borderline minimum distance information for all Voronoi cells of the entire network, and thus, the distance due to POI expansion when performing the nearest point query. No update operation is required.

In addition, the time to calculate the minimum distance from the query point to the POI when performing the nearest-neighbor query corresponds to the time required to access and retrieve the storage that maintains the boundary minimum distance information, and the minimum distance between the boundary points is expressed in matrix units. It is easy to access the minimum distance.

Therefore, the present invention does not require a direct minimum distance operation and does not require a distance update operation according to the POI extension when performing the nearest-contact query. Thus, the total number of distance operations is significantly reduced, the comparison operation cost is reduced, and the nearest-contact query processing time. This can shorten the effect.

Claims (15)

In the road-wide network to which the Voronoi diagram is applied, the storage unit stores boundary minimum distance information including a minimum distance matrix between boundary points of the Voronoi cell; And, The nearest query processing unit which processes a predetermined number of nearest neighbor queries using the minimum boundary distance information stored in the storage unit and provides a POI corresponding to the processed query result. Nearest point navigation system based on Voronoi diagram, including. The method of claim 1, The storage unit; A cell information storage unit for storing cell information including boundary points of Voronoi cells in the entire network; A cell minimum distance storage unit for storing cell minimum distance information including a minimum distance between a point of interest (POI) and a node in the Voronoi cell and a minimum distance between the POI and a boundary point; Borderline minimum distance storage unit for storing borderline minimum distance information including the minimum distance matrix between the boundary points in the entire network Nearest point navigation system based on Voronoi diagram, including. The method of claim 2, The nearest query processing unit; According to a query for requesting POIs of a predetermined number of nearest points on a predetermined path, a recent search for a closest point of proximity based on the query point based on cell information, cell minimum distance information, and boundary minimum distance information stored in the storage unit. Nearest point search system based on Voronoi diagram, characterized by providing a contact query algorithm. Maintaining a boundary minimum distance information including a minimum distance matrix between boundary points of a Voronoi cell in a road-wide network to which a Voronoi diagram is applied; Searching for a predetermined number of nearest neighbors corresponding to an arbitrary query point using the boundary minimum distance information; And, Providing a POI corresponding to the searched nearest point with respect to the query point Nearest point search method based on the Voronoi diagram comprising a. The method of claim 4, wherein Cell information including boundary points of Voronoi cells, minimum distance between points of interest (POI) and nodes within each Voronoi cell, and cell minimum distance information including minimum distances between POIs and boundary points for the entire network. Steps to maintain Nearest point search method based on the Voronoi diagram further comprising. The method of claim 5, Maintaining borderline minimum distance information for the entire network; Specifying two different boundary points, Generating at least one distance matrix possible between the two specified boundary points; Setting a minimum distance matrix between the two boundary points having a minimum distance value among the generated at least one distance matrix Nearest point search method based on the Voronoi diagram comprising a. The method of claim 6, The step of setting a minimum distance matrix of at least one distance matrix for the two boundary points, Retrieving an edge including the two specified boundary points; Calculating a minimum distance between nodes constituting the edge and a distance between the node and a boundary point; Calculating a distance between the two boundary points for each distance matrix by using the calculated minimum distance between the nodes and the distance between the node and the boundary point; Setting a distance matrix having a minimum distance among the distance matrices from which the distance between the boundary points is calculated as a minimum distance matrix between the two boundary points; Nearest point search method based on the Voronoi diagram comprising a. The method of claim 7, wherein The distance between two boundary points for each distance matrix is Nearest point search method based on Voronoi diagram, characterized in that calculated by Equation 1. Equation 1: Dx = Dist (n _{(i, x)} , b _i ) + Dist (n _{(i, x)} + n _{(j, x)} ) + Dist (n _{(j, x)} , b _j ) Where x is the number of possible distance matrices between two boundary points, Dx: distance between two boundary points for the distance matrix, b _i (1≤i≤n), b _j (1≤j≤n): two different boundary points, n _{(i, j)} (1≤i≤n, j = 1 | 2): node containing two boundary points, Dist (n _{(i, x)} , b _i ), Dist (n _{(j, x)} , b _j ): distance between the node and the boundary point for the distance matrix x, Dist (n _{(i, x)} + n _{(j, x)} ): distance between nodes for the distance matrix x The method of claim 5, Retrieving a predetermined number of nearest points for any query point; Searching for a Voronoi cell including the query point and setting a POI in the found Voronoi cell as the first nearest point; Searching for the POI having the minimum distance with the query point in sequence with respect to the query point and the neighboring Voronoi cells using the cell information, the minimum distance information of the cell, and the boundary minimum distance information, and setting the next nearest point; Nearest point search method based on the Voronoi diagram comprising a. The method of claim 9, Searching for the POI having the minimum distance with the query point in order and setting the next nearest point, Searching for a Voronoi cell including the query point and calculating a distance A from a boundary point of the found Voronoi cell to the query point; Searching for a minimum distance (B) between a border point of a neighboring Voronoi cell and the Voronoi cell including the query point based on the stored boundary minimum distance information; Searching for a minimum distance (C) between a boundary point of the neighboring Voronoi cell and a POI point of the neighboring Voronoi cell based on cell minimum distance information corresponding to the neighboring Voronoi cell; Calculating a minimum distance from the query point to the POI point using the calculated or retrieved distance values (A), (B), and (C) Nearest point search method based on the Voronoi diagram comprising a. The method of claim 10, Computing the distance (A) from the boundary point of the Voronoi cell including the query point to the query point, When two nodes of the edge including the query point have different Voronoi cells, the distance from the boundary point of the Voronoi cell including the query point to each node is calculated and the distance having the minimum distance among them is calculated. (A) Nearest point search method based on the Voronoi diagram, characterized in that for selecting the distance. The method of claim 11, The distance A from the boundary point of the Voronoi cell including the query point to the query point is Nearest point search method based on the Voronoi diagram, characterized in that calculated by Equation 2. Equation 2: Dist (q, b _i ) = Min (Dist (q, n ₁ ) + Dist (n ₁ , b _i ), Dist (q, n ₂ ) + Dist (n ₂ , b _i )) Where q is the query point, b _i : boundary point of Voronoi cell including query point, Dist (q, b _i ): distance from the boundary point of the Voronoi cell containing the query point to the query point, n ₁ , n ₂ : node containing the query point, Dist (q, n ₁ ), Dist (q, n ₂ ): the distance from the query point to each node, Dist (n ₁ , b _i ), Dist (n ₂ , b _i ): distance from the boundary to each node) The method of claim 10, The minimum distance from the query point to the POI point, The nearest point search method based on a Voronoi diagram, which is calculated by Equation 3. Equation 3: MinDist _{q , p} = Min (Dist (q, b _i ) + Dist (bi, bj) + Dist (bj, p)) Where q is the query point, p: POI point, MinDist _{q , p} : minimum distance from query point to POI point of neighboring Voronoi cells, b _i : boundary point of Voronoi cell including query point, b _j : boundary point of neighboring Voronoi cells, Dist (q, b _i ): distance from the boundary point of the Voronoi cell containing the query point to the query point, Dist (bi, bj): distance between the Voronoi cell containing the query point and the boundary point of the neighboring Voronoi cell, Dist (bj, p): Distance between neighboring Voronoi cells and POI points) The method of claim 10, Searching for the POI having the minimum distance with the query point in order and setting the next nearest point, Calculating a minimum distance from the query point to the POI point for each POI while sequentially expanding the POI based on the query point based on the cell information, the cell minimum distance information, and the boundary minimum distance information; Inserting the calculated minimum distance from the query point to the POI point into a minimum heap for determining the nearest point, and determining the nearest point to the query point in order of distance; Nearest point search method based on the Voronoi diagram further comprising. A computer-readable recording medium in which a program for executing the method of any one of claims 4 to 14 is recorded.

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