JP2013164693A - Calculation apparatus, calculation program, and calculation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To inhibit a reduction in an accuracy of a distance calculation result.SOLUTION: A calculation apparatus 10 has a selection section 15b, a first calculation section 15c, a second calculation section 15d, and a third calculation section 15e. The selection section 15b selects a plurality of groups each having a plurality of nodes among a plurality of nodes, on the basis of adjacency matrix data. The first calculation section 15c calculates an average distance between nodes for each of the plurality of selected groups. The second calculation section 15d calculates a distance between each of the groups and each of the plurality of nodes, on the basis of the average distance between nodes calculated for each group and the adjacency matrix data. The third calculation section 15e calculates a distance between the two nodes between which the distance is to be calculated, on the basis of the calculated distance.

Description

  The present invention relates to a calculation device, a calculation program, and a calculation method.

  Conventionally, there is an apparatus for calculating a distance between nodes in graph data including information indicating each of a large number of nodes and information indicating an edge connecting the nodes. Note that the node in the graph data corresponds to, for example, “person” in Facebook (registered trademark). In this case, the smaller the distance between the nodes, the closer the “persons” indicated by the two nodes are in a friend relationship. An example of the graph data is adjacency matrix data. The adjacency matrix is a value indicating that two nodes are connected, and the value of the component (element) corresponding to the nodes directly connected via the edge corresponds to the unconnected nodes. Indicates a matrix whose value is a value indicating that the two nodes are not connected. An example of “a value indicating that two nodes are connected” is “1”. An example of “a value indicating that two nodes are not connected” is “0”. In addition, the distance between the nodes here is a path connecting two nodes, that is, when there are a plurality of edges and node patterns connecting the two nodes, the distance between the edges in the pattern having the shortest number of edges. Indicates a number.

  Here, by simply deriving all possible paths between the two nodes whose distances are to be calculated, and identifying the path when the number of edges is the shortest from all the derived paths, the node A method of calculating the distance between them is conceivable. However, in this method, the amount of calculation increases as the number of paths in the graph data increases.

  Therefore, the distance between all the nodes is calculated in advance, the calculated distance is stored in the storage device, and when the two nodes to be calculated are designated, the distance corresponding to the two nodes is calculated. A method of calculating the distance between nodes by acquiring from a storage device is also conceivable. In this method, since the distances between all the nodes are stored in advance in the storage device, the amount of calculation can be suppressed. However, with this method, it takes a lot of time to calculate the distances between all the nodes in advance, and the number of combinations of nodes to be stored becomes enormous, which is difficult to realize.

  Therefore, for example, the above-described conventional apparatus selects a predetermined node connected to more edges as a “landmark node” from among a large number of nodes, and connects between all nodes. Instead of the distance, the distance between the landmark node and another node is calculated in advance. The conventional apparatus stores the calculated distance between the landmark node and another node in the storage device. Subsequently, when the two nodes whose distances are to be calculated are specified, the conventional apparatus calculates the sum of the distances between the two nodes and the landmarks from the storage device for each landmark. Then, the above-described conventional apparatus calculates the minimum sum value among the distance sums calculated for each landmark as the distance between two designated nodes.

  20A to 20c are diagrams illustrating an example of a distance calculation method using a conventional device. FIG. 20A shows nodes indicated by the graph data 80 and edges connecting the nodes. In the example of FIG. 20A, a case where nodes 83 and 84 are selected as landmark nodes is shown. Although not shown in the example of FIG. 20A, it is assumed here that nodes other than the nodes 83 and 84 are also selected as landmark nodes. In the example of FIG. 20A, the distance from the node 83 is “2”, the distance from the node 84 is “2”, and the distance from the node 83 is “2”. A node 82 having a distance of “3” is shown. FIG. 20B is a diagram showing the distance between each selected landmark node and each node. The example in FIG. 20B indicates that the distance between the landmark node 83 and the node 81 is “2”. 20B indicates that the distance between the landmark node 83 and the node 82 is “2”. The example of FIG. 20B indicates that the distance between the landmark node 84 and the node 81 is “2”. The example of FIG. 20B indicates that the distance between the landmark node 84 and the node 82 is “3”.

  FIG. 20C shows an example of the sum of the distances between each landmark and each of the two nodes designated as targets for calculating the distance. Here, a case will be described in which nodes 81 and 82 are designated as the two nodes whose distances are to be calculated. In the example of FIG. 20C, the case where the sum of the distance between the node 81 and the landmark node 83 and the distance between the node 82 and the landmark node 83 is “4” is shown. 20C shows a case where the sum of the distance between the node 81 and the landmark node 84 and the distance between the node 82 and the landmark node 84 is “5”. In the case of the example of FIG. 20C, the conventional apparatus calculates “4” as the distance between the node 81 and the node 82.

M. Potamias et al., “Fast Shortest Path Distance Estimation in Large Networks”, CIKM’09, 2009

  However, the above-described conventional apparatus has a problem that the accuracy of the distance calculation result may be lowered.

  An example will be described. FIGS. 21A to 21C, FIGS. 22A to 22C, and FIG. 23 are diagrams for explaining an example of a problem of a conventional device. The example of FIG. 21A shows a case where a node 87 and a node 88 are connected to a node 86 selected as a landmark node in the graph data 85 via an edge. In the example of FIG. 21A, the node 87 and the node 88 are not directly connected via an edge. In the example of FIG. 21A, a node 89 is connected to the node 87 via an edge.

  FIG. 21B is a diagram showing an actual distance between nodes in the case of FIG. 21A. The example of FIG. 21B shows a case where the distance between the node 87 and the node 88 is “2”. The example of FIG. 21B shows a case where the distance between the node 87 and the node 86 is “1”. The example of FIG. 21B shows a case where the distance between the node 87 and the node 89 is “1”. The example of FIG. 21B shows a case where the distance between the node 88 and the node 86 is “1”. The example of FIG. 21B shows a case where the distance between the node 88 and the node 89 is “3”. The example of FIG. 21B shows a case where the distance between the node 86 and the node 89 is “2”.

  FIG. 21C is a diagram illustrating the distance between the nodes calculated by the conventional device in the case of FIG. 21A. As illustrated in the example of FIG. 21C, the conventional apparatus calculates the distance “2” between the node 87 and the node 88. Further, as shown in the example of FIG. 21C, the conventional apparatus calculates the distance “1” between the node 87 and the node 86. Further, as illustrated in the example of FIG. 21C, the conventional apparatus calculates the distance “3” between the node 87 and the node 89. Further, as illustrated in the example of FIG. 21C, the conventional apparatus calculates the distance “1” between the node 88 and the node 86. Further, as illustrated in the example of FIG. 21C, the conventional apparatus calculates the distance “3” between the node 88 and the node 89. Further, as illustrated in the example of FIG. 21C, the conventional apparatus calculates the distance “2” between the node 86 and the node 89.

  That is, in the example of FIG. 21A, the calculation result regarding the distance between the nodes 87 and 89 is different from the actual distance, and the calculation result of the distance between the nodes other than between the nodes 87 and 89 is the same as the actual distance. . As described above, the reason why the calculation result is the same as the implementation distance between most nodes is that the nodes 87 and 88 connected to the landmark node 86 are not directly connected via the edge. . The reason why the calculation result of the distance between the nodes 87 and 89 is different from the actual distance is as follows. That is, although the nodes 87 and 89 are directly connected to each other via the edge, in the conventional apparatus, the sum of the distances between the landmark 86 and the nodes 87 and 89 is the same between the nodes 87 and 89. The reason is that it is calculated as a distance.

  The example of FIG. 22A shows a case where a node 92 and a node 93 are connected to a node 91 selected as a landmark node in the graph data 90 via an edge. In the example of FIG. 22A, the node 92 and the node 93 are directly connected via an edge. In the example of FIG. 22A, a node 94 is connected to the node 92 via an edge.

  FIG. 22B is a diagram illustrating an actual distance between nodes in the case of FIG. 22A. The example of FIG. 22B shows a case where the distance between the node 92 and the node 93 is “1”. The example of FIG. 22B shows a case where the distance between the node 92 and the node 91 is “1”. The example of FIG. 22B shows a case where the distance between the node 92 and the node 94 is “1”. Further, the example of FIG. 22B shows a case where the distance between the node 93 and the node 91 is “1”. The example of FIG. 22B shows a case where the distance between the node 93 and the node 94 is “2”. The example of FIG. 22B shows a case where the distance between the node 91 and the node 94 is “2”.

  FIG. 22C is a diagram illustrating the distance between the nodes calculated by the conventional apparatus in the case of FIG. 22A. As illustrated in the example of FIG. 22C, the conventional device calculates the distance “2” between the node 92 and the node 93. Further, as illustrated in the example of FIG. 22C, the conventional apparatus calculates the distance “1” between the node 92 and the node 91. Further, as illustrated in the example of FIG. 22C, the conventional apparatus calculates the distance “3” between the node 92 and the node 94. Further, as illustrated in the example of FIG. 22C, the conventional apparatus calculates the distance “1” between the node 93 and the node 91. Further, as shown in the example of FIG. 22C, the conventional apparatus calculates the distance “3” between the node 93 and the node 94. Further, as illustrated in the example of FIG. 22C, the conventional apparatus calculates the distance “2” between the node 91 and the node 94.

  That is, in the example of FIG. 22A, the calculation results of the distances between the nodes 92 and 93, between the nodes 92 and 94, and between the nodes 93 and 94 are different from the actual distance. In this way, the distance calculated by the conventional apparatus is more likely to be different from the actual distance in the example in FIG. 22A compared to the example in FIG. 21A. One reason for this will be described. In the example of FIG. 22A, the nodes 92 and 93 connected to the landmark node 91 are directly connected via an edge. Therefore, the actual distance between the nodes 92 and 93, between the nodes 92 and 94, and between the nodes 93 and 94 is a distance indicated by a route that does not pass through the landmark node 91. However, in the example of FIG. 22A, the conventional apparatus calculates the sum of the distance between the landmark node 91 and each node, that is, the distance indicated by the route passing through the landmark node 91 as the distance between the nodes. End up. As described above, in the conventional apparatus, when nodes connected to the landmark node are directly connected via an edge, there is a high possibility that the calculated distance is different from the actual distance.

  For example, as shown in FIG. 23, when nodes connected to the landmark node are connected and the graph diameter is small, there is a high possibility that the distance calculated by the conventional apparatus is different from the actual distance. In the example of FIG. 23, the correct answer rate (number of correct answers / number of all pairs of nodes) calculated by a conventional apparatus is about 0.51 (630/1225), which is only about half. The graph diameter refers to the maximum distance among the distances between all nodes in the graph indicated by the graph data. In the example of FIG. 23, the node is represented as “N”, and the landmark node is represented as “LM”.

  The disclosed technique has been made in view of the above, and an object thereof is to provide a calculation device, a calculation program, and a calculation method that can suppress a decrease in accuracy of a distance calculation result.

  The calculation device disclosed in the present application includes a selection unit, a first calculation unit, a second calculation unit, and a third calculation unit. The selection unit selects a plurality of groups each having a plurality of nodes from the plurality of nodes based on information indicating a connection state between the nodes in the graph having the plurality of nodes. The first calculation unit calculates an average distance between nodes in the group for each of the plurality of groups selected by the selection unit. Based on the average distance between the nodes in the group calculated for each group by the first calculation unit, and information indicating the connection state between the nodes, the second calculation unit Calculate the distance to each of. The third calculation unit calculates the distance between the two nodes whose distances are to be calculated based on the distance calculated by the second calculation unit.

  Moreover, the calculation device disclosed in the present application includes a selection unit, a first calculation unit, and a second calculation unit. The selection unit calculates each of a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from a matrix indicating a connection state between nodes in a graph having a plurality of nodes. Then, the selection unit selects a plurality of groups each having a plurality of nodes based on the plurality of calculated eigenvalues and the plurality of eigenvectors. The first calculation unit calculates a distance between each of the plurality of groups and each of the plurality of nodes based on the eigenvalue and the eigenvector. The second calculation unit calculates a distance between two nodes whose distances are to be calculated based on the distance calculated by the first calculation unit.

  Moreover, the calculation device disclosed in the present application includes a first calculation unit and a second calculation unit. The first calculation unit calculates each of a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from a matrix indicating a connection state between nodes in a graph having a plurality of nodes. The second calculation unit calculates, for each of a plurality of eigenvectors, a product of the product of the two components of the eigenvector corresponding to each of the two nodes whose distances are to be calculated and the value of the eigenvalue corresponding to the eigenvector to the k-th power. . The second calculation unit calculates the sum of the products calculated for each of the plurality of eigenvectors. Subsequently, the second calculation unit calculates a minimum value of the k between the two nodes that exceeds a value obtained by subtracting a predetermined value from a value indicating that the nodes are connected in the matrix. Is calculated as a distance.

  According to one aspect of the calculation device disclosed in the present application, it is possible to suppress a decrease in the accuracy of the distance calculation result.

FIG. 1 is a diagram illustrating an example of a functional configuration of the calculation apparatus according to the first embodiment. FIG. 2 is a diagram illustrating an example of a data configuration of adjacency matrix data. FIG. 3 is a diagram illustrating an example of a data configuration of distance information. FIG. 4 is a diagram for explaining an example of processing executed by the calculation apparatus according to the first embodiment. FIG. 5 is a diagram for explaining an example of processing executed by the calculation apparatus according to the first embodiment. FIG. 6 is a schematic diagram illustrating an example of a process executed by the calculation apparatus according to the first embodiment. FIG. 7 is a flowchart illustrating a procedure of distance information calculation processing according to the first embodiment. FIG. 8 is a flowchart illustrating the procedure of the calculation process according to the first embodiment. FIG. 9 is a diagram illustrating an example of a functional configuration of the calculation apparatus according to the second embodiment. FIG. 10 is a diagram illustrating an example of the adjacency matrix. FIG. 11A is a diagram illustrating an example of eigenvalues and eigenvectors. FIG. 11B is a diagram illustrating an example of the reciprocal of the square root of the absolute value of the eigenvalue. FIG. 12 is a diagram for explaining an example of a distance calculation method. FIG. 13 is a flowchart illustrating a procedure of distance information calculation processing according to the second embodiment. FIG. 14 is a diagram illustrating an example of a functional configuration of the calculation apparatus according to the third embodiment. FIG. 15 is a diagram for explaining an example of a process executed by the calculation apparatus according to the third embodiment. FIG. 16 is a schematic diagram illustrating an example of a process executed by the calculation apparatus according to the third embodiment. FIG. 17 is a flowchart illustrating a procedure of matrix information calculation processing according to the third embodiment. FIG. 18 is a flowchart illustrating the procedure of the calculation process according to the third embodiment. FIG. 19 is a diagram illustrating a computer that executes a calculation program. FIG. 20A is a diagram illustrating an example of a distance calculation method by a conventional device. FIG. 20B is a diagram illustrating an example of a distance calculation method performed by a conventional device. FIG. 20C is a diagram illustrating an example of a distance calculation method by a conventional device. FIG. 21A is a diagram for explaining an example of a problem of a conventional device. FIG. 21B is a diagram for explaining an example of a problem of a conventional device. FIG. 21C is a diagram for explaining an example of a problem of the conventional device. FIG. 22A is a diagram for explaining an example of a problem of a conventional device. FIG. 22B is a diagram for explaining an example of a problem of the conventional device. FIG. 22C is a diagram for describing an example of a problem of a conventional device. FIG. 23 is a diagram for explaining an example of a problem of a conventional apparatus.

  Hereinafter, embodiments of a calculation apparatus, a calculation program, and a calculation method disclosed in the present application will be described in detail with reference to the drawings. The embodiments do not limit the disclosed technology. In addition, the embodiments can be appropriately combined within a range in which processing contents are not contradictory.

  A calculation apparatus according to the first embodiment will be described. FIG. 1 is a diagram illustrating an example of a functional configuration of the calculation apparatus according to the first embodiment.

[Functional structure of calculation device]
As illustrated in FIG. 1, the calculation device 10 includes an input unit 11, an output unit 12, a communication unit 13, a storage unit 14, and a control unit 15.

  The input unit 11 inputs various information to the control unit 15. For example, the input unit 11 receives an instruction for executing a calculation process described later from the user, and inputs the received instruction to the control unit 15. This instruction includes IDs (IDentification) of two nodes (node pairs) for which distances are to be calculated. Further, the input unit 11 receives an instruction for executing distance information calculation processing described later from the user, and inputs the received instruction to the control unit 15. The input unit 11 receives various instructions from the user and inputs the received instructions to the control unit 15. Further, the input unit 11 receives an adjacency matrix data 14b described later from the user, and inputs the received adjacency matrix data 14b to the control unit 15. In addition, the input unit 11 receives an instruction from the user to acquire the adjacency matrix data 14 b from an external server, and inputs the received instruction to the control unit 15. As an example of the device of the input unit 11, there is a device that accepts a user operation such as a mouse or a keyboard.

  The output unit 12 outputs various information. For example, the output unit 12 displays the distance between two nodes under the control of an output control unit 15f described later. An example of the device of the output unit 12 is a liquid crystal display.

  The communication unit 13 is an interface for performing communication between devices. For example, the communication unit 13 is connected to a server (not shown). As an example of such a server, a server that transmits the adjacency matrix data 14b to the calculation device 10 when an instruction to transmit the adjacency matrix data 14b described later to the calculation device 10 is received. Further, when receiving the adjacency matrix data 14 b from the server, the communication unit 13 transmits the received adjacency matrix data 14 b to the control unit 15.

  The storage unit 14 stores various information. For example, the storage unit 14 stores adjacency matrix data 14b and distance information 14b.

  The adjacency matrix data 14b is an example of graph data indicating a connection state between nodes in a graph having a plurality of nodes. The adjacency matrix indicated by the adjacency matrix data 14b is a matrix having values indicating that two nodes are connected as values of components corresponding to two nodes directly connected via an edge. The adjacency matrix is a matrix having values indicating that two nodes are not connected as values of components corresponding to nodes that are not connected. FIG. 2 is a diagram illustrating an example of a data configuration of adjacency matrix data. In the following description, the node may be expressed as “N”. 2, N2, N3, and N4 are connected to N1, N1 and N4 are connected to N2, N1 is connected to N3, and N1 and N2 are connected to N4. Next, the adjacency matrix data 14b in the case of a simple graph will be described. In the case of such a graph, the adjacency matrix indicated by the adjacency matrix data 14b shown on the right side in FIG. 2 has two nodes connected as values of components between the nodes N1 and N2, N1 and N3, and N1 and N4. For example, “1”. Further, the adjacency matrix indicated by the adjacency matrix data 14b shown on the right side in FIG. 2 has a value indicating that two nodes are connected, for example, “1” as the value of the component between the nodes N2 and N4. . On the right side in FIG. 2, the adjacency matrix indicated by the adjacency matrix data 14b is “1” as the value of the component between the same nodes (N1 and N1, N2 and N2, N3 and N3, N4 and N4). The case of having is shown.

  The distance information 14b is information indicating the distance between each landmark node group described later and each node. The distance information 14b is calculated by a second calculation unit 15d described later. FIG. 3 is a diagram illustrating an example of a data configuration of distance information. In the following description, a landmark node group to be described later may be referred to as “LMG”. In the example of FIG. 3, the case where the distance information 14b indicates that the distance between N1 and LMG1 is “0.7” is shown. In the example of FIG. 3, the distance information 14b indicates a case where the distance between N1 and LMG2 indicates “1.7”.

  The storage unit 14 is, for example, a semiconductor memory device such as a flash memory, or a storage device such as a hard disk or an optical disk. The storage unit 14 is not limited to the above type of storage device, and may be a RAM (Random Access Memory) or a ROM (Read Only Memory).

  The control unit 15 has an internal memory for storing programs defining various processing procedures and control data, and executes various processes using these. As shown in FIG. 1, the control unit 15 includes an acquisition unit 15a, a selection unit 15b, a first calculation unit 15c, a second calculation unit 15d, a third calculation unit 15e, and an output control unit 15f. And have.

  The acquisition unit 15a acquires adjacency matrix data 14b. For example, when the adjacency matrix data 14 b is input from the input unit 11, the acquisition unit 15 a acquires the input adjacency matrix data 14 b and stores the acquired adjacency matrix data 14 b in the storage unit 14. In addition, when an instruction to acquire the adjacency matrix data 14b from an external server is input from the input unit 11, the acquisition unit 15a transmits an instruction to transmit the adjacency matrix data 14b to the calculation device 10 to the communication unit 13. To do. Further, when receiving the adjacency matrix data 14 b from the communication unit 13, the acquisition unit 15 a acquires the received adjacency matrix data 14 b and stores the acquired adjacency matrix data 14 b in the storage unit 14.

  The selection unit 15b selects various information. For example, the selection unit 15b selects a plurality of landmark node groups each having a plurality of nodes from the plurality of nodes based on the adjacency matrix data 14b indicating the connection state between the nodes in the graph having the plurality of nodes. To do.

  If it demonstrates with a specific example, the selection part 15b will acquire the adjacency matrix data 14b from the memory | storage part 14 first. Then, the selection unit 15b selects a predetermined number of landmark nodes using a known technique described in “Fast Shortest Path Distance Estimation in Large Networks” or the like. For example, the selection unit 15b counts the number of nodes connected to each node from the adjacent state between the nodes in the graph indicated by the adjacency matrix data 14b, and performs the following processing in descending order of the number of connected nodes. I do. That is, the selection unit 15b selects a predetermined number of nodes as landmark nodes from the nodes having the largest number of connected nodes. FIG. 4 is a diagram for explaining an example of processing executed by the calculation apparatus according to the first embodiment. In the example of the graph illustrated in FIG. 4, the selection unit 15b includes the top five nodes with the largest number of connected nodes, that is, N8, N18, N28, where the number of connected nodes is “9”, Five nodes N38 and N48 are selected as landmark nodes.

  Next, the selection unit 15b selects a node located at a predetermined distance from the landmark node and the group of the landmark nodes as a landmark node group. In the example shown in the graph of FIG. 4, the selection unit 15b identifies the nodes N1 to N7, N9, and N10 whose distances are “1” from N8, and identifies the identified N1 to N7, N9, and N10 and the landmark node. The landmark node group is selected by determining the group N8 as LMG1. Similarly, in the example shown in the graph of FIG. 4, the selection unit 15b selects LMG2 to LMG5. That is, in the example shown in the graph of FIG. 4, the selection unit 15b selects five landmark node groups.

  The first calculation unit 15c calculates an average distance between nodes in the landmark node group for each of the plurality of landmark node groups selected by the selection unit 15b. A specific example will be described. The first calculation unit 15c includes a landmark node group (an unselected land) that is not selected by the first calculation unit 15c among the plurality of landmark node groups selected by the selection unit 15b. One mark node group) is selected. Then, the first calculation unit 15c calculates the distance between all the nodes in the selected landmark node group. Then, the first calculation unit 15c calculates the sum of the distances between all the calculated nodes, and divides the calculated sum by the number of combinations between all the nodes in the selected landmark node group. Then, the average value of the distances between the nodes in the landmark node group is calculated. The average value of this distance is the average distance. In this way, the first calculation unit 15c calculates the average distance between nodes for all landmark node groups. For example, in the example shown in the graph of FIG. 4, the first calculation unit 15 c calculates an average distance “1.4” between nodes for LMG1.

  Based on the average distance between the nodes in the landmark node group calculated by the first calculation unit 15c for each landmark node group and the adjacency matrix data 14b, the second calculation unit 15d Process. That is, the second calculation unit 15d calculates the distance between each of the landmark node groups and each of all the nodes.

  A specific example will be described. The second calculation unit 15d calculates the distance between the landmark node group and the nodes in the landmark node group, and the average distance between the nodes calculated by the first calculation unit 15c for the landmark node group. The value is divided by a predetermined value. FIG. 5 is a diagram for explaining an example of processing executed by the calculation apparatus according to the first embodiment. The example of FIG. 5 shows LMG1 in the example shown by the graph of FIG. 4 and N11 connected to N1 in LMG1. In the example shown in the graph of FIG. 5, the second calculation unit 15d calculates the distance between LMG1 and each of N1 to N10 in LMG1 as follows. That is, the second calculation unit 15d calculates a value “0.7” obtained by dividing the average distance “1.4” between nodes calculated by the first calculation unit 15c for LMG1 by “2”, and LMG1. Calculated as the distance to each of N1 to N10 in LMG1.

  The second calculation unit 15d calculates the distance between the landmark node group and a node that does not belong to the landmark node group as follows. That is, the second calculation unit 15d first identifies a node that is in the landmark node group and is closest to a node that does not belong to the landmark node group. Then, the second calculation unit 15d adds the above-mentioned nodes not belonging to the landmark to a value obtained by dividing the average distance between the nodes calculated by the first calculation unit 15c for the landmark node group by a predetermined value. A value obtained by adding the distance to the identified node is calculated. In this way, the second calculation unit 15d calculates the distance between the landmark node group and a node that does not belong to the landmark node group. In the example shown in the graph of FIG. 5, the second calculation unit 15d calculates the distance between LMG1 and N11 that does not belong to LMG1 as follows. That is, the second calculation unit 15d first identifies N1 that is a node in LMG1 and is closest to N11 that does not belong to LMG1. Then, the second calculation unit 15d belongs to LMG1 to a value “0.7” obtained by dividing the average distance “1.4” between the nodes calculated by the first calculation unit 15c for LMG1 by “2”. A value “1.7” obtained by adding the distance “1” between the node N1 that is not present and the identified node N1 is calculated. In this way, the second calculation unit 15d calculates the distance between LMG1 and N11 that does not belong to LMG1.

  Further, the second calculation unit 15d calculates the distance between each of the landmark node groups and each of all the nodes by the same method as described above. Then, the second calculation unit 15d stores distance information 14b, which is information indicating the distance between each of the landmark node groups and each of all the nodes, in the storage unit 14.

The third calculation unit 15e calculates a distance between two nodes whose distances are to be calculated based on the distance calculated by the second calculation unit 15d. A specific example will be described. When an instruction for executing the calculation process is input from the input unit 11, the third calculation unit 15 e first determines from the IDs of two nodes (node pairs) that are included in the instruction and are distance calculation targets. Identify two nodes. Hereinafter, a case where the two specified nodes are N _A and N _B will be described. Then, the third calculation unit 15e acquires the distance information 14b from the storage unit 14.

Next, the third calculation unit 15e selects one unselected landmark node group. Then, a third calculation unit 15e refers to the acquired distance information 14b, specifies the distance "D _A" of the landmark node group and the selected node N _A. The third calculation unit 15e refers to the acquired distance information 14b, specifies the distance "D _B" in the landmark node group and the selected node N _B. Then, a third calculation unit 15e calculates the distance sum _"D A + _{D B"} in the _{"D A"} and the distance _{"D B"} as the distance of the candidate. The third calculation unit 15e sequentially selects all the landmark node groups one by one, performs the same process, and calculates distance candidates for all the landmark node groups.

  FIG. 6 is a schematic diagram illustrating an example of a process executed by the calculation apparatus according to the first embodiment. Referring to FIG. 6, N2 and N12 are identified from the IDs of the two nodes included in the input instruction, and the distance between N2 and N12 is calculated using distance information 14b shown in the example of FIG. The case will be described. As shown in the example of FIG. 6, the third calculation unit 15e calculates the sum “3.4” of the distance “0.7” between LMG1 and N2 and the distance “2.7” between LMG1 and N12. , N2 and N12 are calculated as candidate distances. Further, as illustrated in the example of FIG. 6, the third calculation unit 15 e adds the distance “2.7” between LMG2 and N2 and the sum “3.4” of the distance “0.7” between LMG2 and N12. Is calculated as a distance candidate between N2 and N12. Further, as illustrated in the example of FIG. 6, the third calculation unit 15 e adds the distance “1.7” between the LMG 3 and N 2 and the sum “3.4” of the distance “1.7” between the LMG 3 and N 12. Is calculated as a distance candidate between N2 and N12. Further, as illustrated in the example of FIG. 6, the third calculation unit 15 e adds the distance “2.7” between the LMG 4 and N 2 and the distance “2.7” between the LMG 4 and N 12 to “5.4”. Is calculated as a distance candidate between N2 and N12. Further, as illustrated in the example of FIG. 6, the third calculation unit 15 e has a sum “5.4” of the distance “2.7” between the LMG 5 and N 2 and the distance “2.7” between the LMG 5 and N 12. Is calculated as a distance candidate between N2 and N12.

  Thereafter, the third calculation unit 15e selects a candidate having the shortest distance among the calculated distance candidates. For example, in the example of FIG. 6, the distance candidate “3.4” is selected as the candidate with the shortest distance. Subsequently, the third calculation unit 15e calculates a value obtained by rounding the selected candidate to the first decimal place as a distance between two nodes to be calculated. For example, in the example of FIG. 6, the third calculation unit 15e calculates a value “3” obtained by rounding the selected distance candidate “3.4” to the first decimal place as the distance between N2 and N12. . Note that the third calculation unit 15e can also calculate the selected distance candidate as it is as the distance between two nodes to be calculated.

  The output control unit 15f controls the display by the output unit 12 so as to display the distance between the two nodes calculated by the third calculation unit 15e.

  As described above, the control unit 15 calculates the average distance between the nodes for each landmark node group, and uses the calculated average distance between the nodes to determine the distance between each landmark node group and all the nodes. The distance information 14b including the calculated distance is calculated and stored. Then, the control unit 15b refers to the distance information 14b and calculates the distance between the two nodes. Thus, since the distance information 14b used when calculating the distance between the nodes is calculated based on the average distance between the nodes, the distance between the nodes using the distance between the conventional landmark node and all the nodes. Compared with the case of calculating the distance, the accuracy of the distance calculation result is better. Therefore, according to the control part 15, the fall of the precision of the calculation result of distance can be suppressed.

  The control unit 15 is an integrated circuit such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA) or an electronic circuit such as a central processing unit (CPU) or a micro processing unit (MPU).

[Process flow]
Next, a processing flow of the calculation apparatus 10 according to the present embodiment will be described. FIG. 7 is a flowchart illustrating a procedure of distance information calculation processing according to the first embodiment. The distance information calculation process is executed, for example, at a timing when the control unit 15 receives an instruction for executing the distance information calculation process from the input unit 11.

  As illustrated in FIG. 7, the selection unit 15b acquires the adjacency matrix data 14b from the storage unit 14 (S101). Then, the selection unit 15b selects a predetermined number of landmark nodes, and performs the following process for each of the selected predetermined number of landmark nodes. That is, the selection unit 15b selects a node located at a predetermined distance from the landmark node and a group of the landmark nodes as a landmark node group (S102).

  Subsequently, the first calculation unit 15c determines whether there is a landmark node group that has not been selected in S104, which will be described later, among the plurality of landmark node groups selected by the selection unit 15b (S103). When there is an unselected landmark node group (Yes in S103), the first calculation unit 15c selects one unselected landmark node group (S104). Then, the first calculation unit 15c calculates the distance between all the nodes in the selected landmark node group, calculates the sum of the calculated distances between all the nodes, and then performs the following processing I do. That is, the first calculation unit 15c divides the calculated sum by the number of combinations between all the nodes in the selected landmark node group, thereby calculating the average value of the distances between the nodes in the landmark node group. (Average distance) is calculated (S105).

  Then, the second calculation unit 15d calculates the following based on the average distance between the nodes in the landmark node group calculated for each landmark node group by the first calculation unit 15c, and the adjacency matrix data 14b. Perform the following process. That is, the second calculation unit 15d calculates the distance between each of the landmark node groups and all the nodes (S106), and returns to S103.

  On the other hand, when there is no unselected landmark node group (No in S103), the second calculation unit 15d has distance information 14b that is information indicating the distance between each of the landmark node groups and each of all the nodes. Is stored in the storage unit 14 (S107), and the process is terminated.

  FIG. 8 is a flowchart illustrating the procedure of the calculation process according to the first embodiment. The calculation process is executed, for example, at a timing when the control unit 15 receives an instruction to execute the calculation process from the input unit 11.

As illustrated in FIG. 8, the third calculation unit 15 e identifies two nodes N _A and N _B from the IDs of the two nodes whose distances are to be calculated included in the instruction for executing the calculation process. (S201). And the 3rd calculation part 15e acquires the distance information 14b from the memory | storage part 14 (S202).

Next, the third calculation unit 15e determines whether there is a landmark node group that has not been selected in S204, which will be described later (S203). One unselected landmark node group is selected (S204). Then, a third calculation unit 15e refers to the acquired distance information 14b, specifies the distance _{"D A"} of the landmark node group and the selected node _{N A} (S205). Then, a third calculation unit 15e refers to the acquired distance information 14b, specifies the distance "D _B" in the landmark node group and the selected node N _B (S206). Then, a third calculation unit 15e, the distance is calculated as the sum _"D A + _{D B"} distances of the candidate with _{"D A"} and the distance _{"D B"} (S207), returns to S203.

  Thereafter, the third calculation unit 15e selects the candidate with the shortest distance among the calculated distance candidates (S208). Subsequently, the third calculation unit 15e calculates a value obtained by rounding the selected candidate to the first decimal place as the distance between the two nodes to be calculated (S209).

  Then, the output control unit 15f controls the display by the output unit 12 so as to display the distance between the two nodes calculated by the third calculation unit 15e (S210), and ends the process.

  As described above, the calculation device 10 according to the present embodiment calculates a plurality of nodes from among the plurality of nodes based on the adjacency matrix data 14b indicating the connection state between the nodes in the graph having the plurality of nodes. A plurality of landmark node groups are selected. Then, the calculation device 10 calculates the average distance between the nodes in the landmark node group for each of the plurality of selected landmark node groups. Subsequently, the calculation apparatus 10 uses the average distance between the nodes in the landmark node group and the adjacency matrix data 14b, and distance information 14b indicating the distance between each of the landmark node groups and each of all the nodes. calculate. Thereafter, the calculation device 10 calculates the distance between the two nodes whose distance is to be calculated based on the calculated distance information 14b. Thus, since the distance information 14b used when calculating the distance between the nodes is calculated based on the average distance between the nodes, the distance between the nodes using the distance between the conventional landmark node and all the nodes. Compared with the case of calculating the distance, the accuracy of the distance calculation result is better. Therefore, according to the calculation device 10, it is possible to suppress a decrease in accuracy of the distance calculation result.

  In the second embodiment, a case will be described in which eigenvalues and eigenvectors of an adjacency matrix are calculated, and a distance between two nodes is calculated based on the calculated eigenvalues and eigenvectors.

[Configuration of Calculation Device 20]
FIG. 9 is a diagram illustrating an example of a functional configuration of the calculation apparatus according to the second embodiment. As illustrated in FIG. 9, the calculation device 20 includes a storage unit 24 and a control unit 25. The storage unit 24 is different from the storage unit 14 according to the first embodiment in that eigenvalue data 24a and eigenvector data 24b are stored in addition to the storage contents of the storage unit 14 according to the first embodiment illustrated in FIG. The eigenvalue data 24a and eigenvector data 24b will be described later. Moreover, the control part 25 has the point which has the selection part 25a, the 1st calculation part 25b, the 2nd calculation part 25c, and the output control part 25d compared with the control part 15 which concerns on Example 1 shown in FIG. Different. In the following description, the same reference numerals as those in FIG. 1 are given to the respective units and devices that perform the same functions as those in the first embodiment, and the description thereof will be omitted.

  The selection unit 25a calculates each of a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from the adjacency matrix indicated by the adjacency matrix data 14b, and based on the calculated plurality of eigenvalues and the plurality of eigenvectors, Select a landmark node group.

  To describe a specific example, the selection unit 25a first acquires the adjacency matrix data 14b from the storage unit 14. Then, the selection unit 25a calculates the eigenvalue of the adjacency matrix indicated by the adjacency matrix data 14b. FIG. 10 is a diagram illustrating an example of the adjacency matrix. FIG. 10 shows an adjacency matrix indicating connection states between 50 nodes N1 to N50. For example, when the adjacency matrix data 14b indicating the adjacency matrix in the example of FIG. 10 is acquired, the selection unit 25a calculates 50 eigenvalues when the eigenvectors of the adjacency matrix do not overlap. Then, the selection unit 25a specifies the eigenvalues from the largest eigenvalue to a predetermined number from the calculated eigenvalues in descending order, and stores the specified eigenvalue data in the storage unit 24 as eigenvalue data 24a. . For example, the selection unit 25a identifies the top five eigenvalues. FIG. 11A is a diagram illustrating an example of eigenvalues and eigenvectors. The example of FIG. 11A shows a case where the selection unit 25a specifies the top five eigenvalues having the largest absolute value from the calculated eigenvalues. In the following description, a case will be described in which the selection unit 25a identifies the top five eigenvalues with large absolute values. Further, the example of FIG. 11A shows a case where the values of the top five eigenvalues are all “10”.

And the selection part 25a will perform the following processes, if an eigenvalue is specified. That is, the selection unit 25a first sets the value of the variable n to 0. Then, the selection unit 25a determines whether there is an unselected eigenvalue among the top five eigenvalues. When there is an unselected eigenvalue, the selection unit 25a increments the value of the variable n by one. Then, the selection unit 25a selects one of the eigenvalues of unselected as eigenvalues E _n. In the example of FIG. 11A, the selection unit 25a is, first, the case of selecting the "10" one of the eigenvalues of unselected as eigenvalues E ₁ is shown.

Subsequently, the selection unit 25a calculates the eigenvectors V _n corresponding to eigenvalues E _n selected, stored in the storage unit 24 the data of the calculated eigenvectors as unique vector data 24b. In the example of FIG. 11A, the selection unit 25a is, when calculating the eigenvectors V _n corresponding to eigenvalues E ₁ selected is shown. Subsequently, the selection unit 25a, the absolute value, the absolute value of the reciprocal of the square root of the eigenvalues ^{_{E n (1 / (E n}} ) 1/2) identifying the components of a larger eigenvectors _{V n.} FIG. 11B is a diagram illustrating an example of the reciprocal of the square root of the absolute value of the eigenvalue. The example of FIG. 11B indicates that when each value of the eigenvalues E _{1 to} E ₅ is “10”, the reciprocal of the square root of the absolute value of each eigenvalue is approximately “0.3”. That is, in the example of FIG. 11A, selection unit 25a, the absolute value, as a component of the inverse "0.3" is greater than the eigenvectors _{V 1} of the absolute value of the square root of the eigenvalues _{E 1,} corresponding to N1 "0.34" Is identified. The selection unit 25a, the absolute value, as a component of the inverse "0.3" is greater than the eigenvectors _{V 1} of the square root of the absolute value of the eigenvalues _{E 1,} to identify the "0.34" corresponding to N2. The selection unit 25a, the absolute value, as a component of the inverse "0.3" is greater than the eigenvectors _{V 1} of the absolute value of the square root of the eigenvalues _{E 1,} to identify the "0.35" corresponding to N3. The selection unit 25a, the absolute value, as a component of the inverse "0.3" is greater than the eigenvectors _{V 1} of the square root of the absolute value of the eigenvalues _{E 1,} to identify the "0.34" corresponding to N4.

Then, the selection unit 25a selects a set of nodes corresponding to the identified component as the landmark node group _Gn . For example, in the example of FIG. 11A, selection unit 25a, a set of nodes N1-N4, it is selected as the landmark node group _{G 1.} Thereby, so-called “dense” nodes can be selected as landmark node groups. Here, “dense nodes” refers to a node group having a large number of connected edges.

The first calculation unit 25b calculates the distance between each of the plurality of landmark node groups and each of the plurality of nodes based on the eigenvalue and the eigenvector. A specific example will be described. The first calculation unit 25b calculates the distance between the landmark node group _Gn selected by the selection unit 25a and each of all the nodes as follows. That is, the first calculation unit 25b, the value of the logarithm to base the absolute value of E _n the absolute value of the components of the node of eigenvectors V _1, minus "-" a value obtained by multiplying, landmark nodes Calculated as the distance between the group _Gn and the node. FIG. 12 is a diagram for explaining an example of a distance calculation method. In the example of FIG. 12, the first calculation unit 25b multiplies the value obtained by taking the logarithm of the absolute value “10” of E ₂ with respect to the absolute value of the N1 component of the eigenvector V ₂ by minus “−”. the value is calculated as the distance between the landmark node group G ₂ and the N1. In this way, the first calculation unit 25b calculates the distance between the landmark node group _Gn selected by the selection unit 25a and each of all the nodes. The first calculation unit 25b stores distance information 14b, which is information indicating the distance between each of the landmark node groups and each of all the nodes, in the storage unit 24. In the second embodiment, instead of the first calculation unit 25b, the first calculation unit 15c and the second calculation unit 15d according to the first embodiment are adopted and selected in the same manner as in the first embodiment. It is also possible to calculate the distance between the landmark node group _Gn and each of all the nodes.

  Since the second calculation unit 25c and the output control unit 25d are the same as the third calculation unit 15e and the output control unit 15f according to the first embodiment, description thereof is omitted.

  The control unit 25 is an integrated circuit such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA), or an electronic circuit such as a central processing unit (CPU) or a micro processing unit (MPU).

[Process flow]
Next, a processing flow of the calculation device 20 according to the present embodiment will be described. FIG. 13 is a flowchart illustrating a procedure of distance information calculation processing according to the second embodiment. The distance information calculation process is executed, for example, at a timing when the control unit 25 receives an instruction for executing the distance information calculation process from the input unit 11.

  As illustrated in FIG. 13, the selection unit 25a acquires the adjacency matrix data 14b from the storage unit 14 (S301). Then, the selection unit 25a calculates the eigenvalue of the adjacency matrix indicated by the adjacency matrix data 14b (S302). Then, the selection unit 25a identifies the top five eigenvalues having a large absolute value from the calculated eigenvalues, and stores the identified eigenvalue data in the storage unit 24 as eigenvalue data 24a (S303). Then, the selection unit 25a sets the value of the variable n to 0 (S304).

Then, the selection unit 25a determines whether there is an unselected eigenvalue among the top five eigenvalues (S305). When there is an unselected eigenvalue (Yes in S305), the selection unit 25a increments the value of the variable n by 1 (S306). Then, the selection unit 25a selects one of the eigenvalues of unselected as the eigenvalues _{E n} (S307).

Subsequently, the selection unit 25a calculates the eigenvectors _{V n} corresponding to eigenvalues _{E n} selected, stored in the storage unit 24 the data of the calculated eigenvectors as unique vector data 24b (S308). Subsequently, the selection unit 25a, the absolute value, the absolute value of the reciprocal of the square root of the eigenvalues ^{_{E n (1 / (E n}} ) 1/2) identifying the components of a larger eigenvectors _{V n} (S309).

Then, the selection unit 25a selects a set of nodes corresponding to the identified component as the landmark node group _Gn (S310). Subsequently, the first calculating unit 25b, the value of the logarithm to base the absolute value of E _n the absolute value of the components of the node of eigenvectors V _1, minus "-" a value obtained by multiplying, landmarks The process of calculating the distance between the node group _Gn and the node is performed for all nodes (S311). Then, the process returns to S305.

  Here, when there is no unselected eigenvalue (No in S305), the first calculation unit 25b stores distance information 14b that is information indicating the distance between each of the landmark node groups and all the nodes. The data is stored in the unit 24 (S312), and the process ends.

  Note that the calculation process is the same as that in the first embodiment, and thus the description thereof is omitted.

  As described above, the calculation device 20 according to the present embodiment calculates a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from the adjacency matrix indicated by the adjacency matrix data 14b. Then, the calculation device 20 selects a landmark node group based on the calculated plural eigenvalues and plural eigenvectors. Then, the calculation device 20 calculates distance information 14b indicating the distance between each of the plurality of landmark node groups and each of the plurality of nodes based on the eigenvalue and the eigenvector. Thereafter, the calculation device 20 calculates the distance between the two nodes whose distance is to be calculated based on the calculated distance information 14b. Thus, since the distance information 14b used when calculating the distance between the nodes is calculated for each landmark node group having “dense” nodes, the accuracy of the distance calculation result is further improved. It becomes. Therefore, according to the calculation device 20, it is possible to suppress a decrease in accuracy of the distance calculation result.

  In the second embodiment, the landmark node group is selected. In the third embodiment, a case where the distance between two nodes is calculated without selecting the landmark node group will be described.

[Configuration of Calculation Device 30]
FIG. 14 is a diagram illustrating an example of a functional configuration of the calculation apparatus according to the third embodiment. As illustrated in FIG. 14, the calculation device 30 includes a storage unit 34 and a control unit 35. The storage unit 34 is different from the storage unit 24 according to the second embodiment in that it stores adjacency matrix data 14b, eigenvalue data 24a, and eigenvector data 24b among the storage contents of the storage unit 24 according to the second embodiment illustrated in FIG. . The control unit 35 is different from the control unit 25 according to the second embodiment illustrated in FIG. 9 in that the control unit 35 includes a first calculation unit 35a, a second calculation unit 35b, and an output control unit 35c. In the following description, the same reference numerals as those in FIGS. 1 and 9 are used for components and devices that perform the same functions as those in the first and second embodiments, and the description thereof is omitted.

  The first calculator 35a calculates a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from the adjacency matrix indicated by the adjacency matrix data 14b.

  A specific example will be described. First, the first calculation unit 35 a first acquires the adjacency matrix data 14 b from the storage unit 34. Then, the first calculator 35a calculates the eigenvalue of the adjacency matrix indicated by the adjacency matrix data 14b. Then, the first calculation unit 35a specifies, from the calculated eigenvalues, the largest eigenvalue to a predetermined number of eigenvalues in descending order of the absolute value. For example, the first calculation unit 35a identifies the top five eigenvalues. In the following description, a case will be described in which the first calculation unit 35a specifies the top five eigenvalues having a large absolute value.

And the 1st calculation part 35a will perform the following processes, if an eigenvalue is specified. That is, the first calculation unit 35a first sets the value of the variable n to 0. Then, the first calculation unit 35a determines whether there is an unselected eigenvalue among the top five eigenvalues. If there is an unselected eigenvalue, the first calculation unit 35a increments the value of the variable n by one. Then, the first calculating unit 35a selects one of the eigenvalues of unselected as eigenvalues E _n.

Subsequently, the first calculating unit 35a calculates the eigenvectors V _n corresponding to eigenvalues E _n selected. Then, the first calculation unit 35a again determines whether there is an unselected eigenvalue among the top five eigenvalues. First calculation unit 35a, until it is determined that no eigenvalue unselected, is incremented by one the value of the variable n, select the eigenvalues E _n unselected, eigenvector V _n corresponding to eigenvalues E _n selected The process of calculating is repeated.

When it is determined that there is no unselected eigenvalue, the first calculation unit 35a performs the following process. That is, the first calculation unit 35a stores the data of the eigenvector V _n (n = 1, 2,... 5) as the eigenvector data 24b in the storage unit 34, and the eigenvalue E _n (n = 1, 2,. ... 5) is stored in the storage unit 34 as the eigenvalue data 24a.

Second calculating unit 35b, a plurality of eigenvectors _{V n (n = 1,2, ···} 5) each, the distance the product of two components of the eigenvector _{V n} corresponding to each of the two nodes to be calculated for And the product of the eigenvalue E _n corresponding to the eigenvector V _n and the value of the k-th power. Then, the second calculation unit 35b calculates the sum of the value of the product calculated for each of the plurality of eigenvectors V _n. Subsequently, in the second calculation unit 35b, the calculated sum exceeds the value “1-α” obtained by subtracting the predetermined value “α” from the value “1” indicating that the nodes are connected in the adjacent matrix. The minimum value of k is calculated as the distance between the two nodes.

A specific example will be described. When an instruction for executing a calculation process is input from the input unit 11, the second calculation unit 35 b first determines from the IDs of two nodes (node pairs) that are included in the instruction and are distance calculation targets. Identify two nodes. Hereinafter, a case where the two specified nodes are N _A and N _B will be described. Then, the second calculation unit 35b acquires the eigenvector data 24b and the eigenvalue data 24a from the storage unit 34. Next, the second calculation unit 35b sets the value of the variable k to 0.

Thereafter, the second calculation unit 35b increments the value of the variable k by one. Then, the second calculation unit 35b calculates the value of “J” by the following equation.

Here, when the adjacency matrix is “A”, the matrix in which the eigenvectors of the adjacency matrix A are arranged in the column direction is “P”, the inverse matrix of the matrix P is “P ⁻¹ ”, and P ⁻¹ AP = W, the matrix W Is a matrix in which diagonal components have eigenvalues and the other components are “0”. Further, since A = PWP ⁻¹ , A ^k = PW ^k P ⁻¹ . Furthermore, since the value of k when the component indicating the connection state between two nodes is “1” or more in the matrix indicated by A ^k indicates the distance between the two nodes, It is an approximate expression of ^k .

FIGS. 15 and 16 are diagrams for explaining an example of processing executed by the calculation apparatus according to the third embodiment. The example of FIG. 15 illustrates a case where the second calculation unit 35b identifies N1 and N25 from the IDs of two nodes that are distance calculation targets included in the instruction for executing the calculation process. Further, the example of FIG. 15 illustrates components N1 and N25 in each of the eigenvectors V _{1 to} V ₅ among the eigenvector components indicated by the eigenvector data 24b acquired by the second calculation unit 35b. The example of FIG. 15 illustrates a case where each of the eigenvalues E _{1 to} E ₅ indicated by the eigenvalue data 24a acquired by the second calculation unit 35b is “10”. In the example of FIG. 15, when k = 1, the second calculation unit 35 b performs the calculation indicated by the top expression in FIG. 16. At this time, the value of J is 0.01.

Then, the second calculation unit 35b determines whether or not the value of J is “1−α” or more. Here, “1” is a value indicating that the nodes are connected in the adjacency matrix. In the "1" but the reason for the comparison between J and "1-alpha" is a approximate expression of the equation is A ^k, the diagonal elements of the matrix W, the first calculation unit This is because eigenvalues other than the predetermined number (five in this embodiment) of eigenvalues specified by 35a are also included.

  When the value of J is not “1−α” or more, the second calculation unit 35b increments the value of k by one, calculates the value of J again using the above equation, It is determined whether or not the calculated value of J is “1−α” or more. In this way, the second calculation unit 35b increments the value of k by one until the calculated value of J becomes “1−α” or more, and repeats the process of calculating J by the above formula.

  For example, in the example of FIG. 16, when k = 1, the value of J is 0.01, and the value of J is not “1−α” or more. And calculate the value of J again. Here, in the example of FIG. 15, when k = 2, the second calculation unit 35b performs the calculation indicated by the central expression in FIG. At this time, the value of J is 0.12, and since the value of J is not “1−α” or more, the second calculation unit 35b sets k = 3 and calculates the value of J again. To do. In the example of FIG. 16, when k = 3, the value of J is 1.22, and the value of J is “1−α” or more.

When the value of J is “1−α” or more, the second calculation unit 35b calculates the value of k as the distance between N _{A and} N _B.

  As described above, the control unit 35 uses the above formula to check the value of k when the value of J is “1−α” or more by increasing from “1” one by one. Therefore, according to the present embodiment, the distance between the nodes can be calculated with high accuracy.

  The output control unit 35c controls the display by the output unit 12 so as to display the distance between the two nodes calculated by the second calculation unit 35b.

  The control unit 35 is an integrated circuit such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA) or an electronic circuit such as a central processing unit (CPU) or a micro processing unit (MPU).

[Process flow]
Next, a processing flow of the calculation device 30 according to the present embodiment will be described. FIG. 17 is a flowchart illustrating a procedure of matrix information calculation processing according to the third embodiment. The matrix information calculation process is executed, for example, at a timing when the control unit 35 receives an instruction to execute the matrix information calculation process from the input unit 11.

  As shown in FIG. 17, the first calculation unit 35a acquires the adjacency matrix data 14b from the storage unit 34 (S401). Then, the first calculator 35a calculates the eigenvalue of the adjacency matrix indicated by the adjacency matrix data 14b (S402). Then, the first calculation unit 35a identifies the top five eigenvalues with large values (S403).

Then, the first calculation unit 35a sets the value of the variable n to 0 (S404). Then, the first calculation unit 35a determines whether there is an unselected eigenvalue among the top five eigenvalues (S405). If there is an unselected eigenvalue (Yes at S405), the first calculation unit 35a increments the value of the variable n by one (S406). Then, the first calculating unit 35a selects one of the eigenvalues of unselected as the eigenvalues _{E n} (S407).

Subsequently, the first calculating unit 35a calculates the eigenvectors _{V n} corresponding to eigenvalues _{E n} selected (S408), returns to S405.

If there is no unselected eigenvalue (No at S405), the first calculation unit 35a performs the following process. That is, the first calculation unit 35a stores the data of the eigenvector V _n (n = 1, 2,... 5) as the eigenvector data 24b in the storage unit 34, and the eigenvalue E _n (n = 1, 2,. .. 5) is stored in the storage unit 34 as the eigenvalue data 24a (S409), and the process is terminated.

  FIG. 18 is a flowchart illustrating the procedure of the calculation process according to the third embodiment. The calculation process is executed, for example, at a timing when the control unit 35 receives an instruction for executing the calculation process from the input unit 11.

As illustrated in FIG. 18, the second calculation unit 35 b determines two nodes (N _A and N _B ) from the IDs of the two nodes that are distance calculation targets included in the instruction for executing the calculation process. Specify (S501). Then, the second calculation unit 35b acquires eigenvector data 24b and eigenvalue data 24a from the storage unit 34 (S502). Next, the second calculation unit 35b sets the value of the variable k to 0 (S503).

  Thereafter, the second calculator 35b increments the value of the variable k by 1 (S504). Then, the second calculator 35b calculates the value of “J” by the above formula (S505).

  Then, the second calculation unit 35b determines whether the value of J is “1−α” or more (S506). If the value of J is not “1−α” or more (No at S506), the process returns to S504.

Here, when the value of J is “1−α” or more (Yes in S506), the second calculation unit 35b calculates the value of k as the distance between N _{A and} N _B (S507). ). Then, the output control unit 35c controls the display by the output unit 12 so as to display the distance between the two nodes calculated in S507 (S508), and ends the process.

As described above, the calculation apparatus 30 according to the present embodiment calculates a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from the adjacency matrix indicated by the adjacency matrix data 14b. Then, the calculation device 30 calculates, for each of a plurality of eigenvectors V _n (n = 1, 2,... 5), the product of two components of the eigenvector V _n corresponding to each of the two nodes whose distances are to be calculated. , and it calculates the product of the k-th power values eigenvalue E _n corresponding to eigenvectors V _n. The calculation device 30 calculates the sum J of the value of the product calculated for each of the plurality of eigenvectors V _n. Subsequently, the calculation device 30 determines that the calculated sum J exceeds the minimum value “1-α” obtained by subtracting the predetermined value “α” from the value “1” indicating that the nodes are connected in the adjacent matrix. The value of k is calculated as the distance between the two nodes. As described above, the calculation device 30 according to the present embodiment examines the value of k when the value of the total sum J is “1−α” or more by increasing one by one from “1”. Therefore, according to the calculation device 30 according to the present embodiment, the distance between nodes can be calculated with high accuracy.

Moreover, the following value can also be used as the value of J. First, calculating device 30, a plurality of eigenvectors _{V n (n = 1,2, ···} 5) each, and the two components of the product of eigenvectors _{V n} corresponding to each of the distance the two nodes to be calculated for , and it calculates the product of the k-th power values eigenvalue E _n corresponding to eigenvectors V _n. Then, the calculation device 30 calculates the average value of the sum of the product values calculated for each of the plurality of eigenvectors V _n , that is, the product calculated using V _n (n = 1), and V _n (n = 1, 2). ), The product sum calculated using V _n (n = 1, 2, 3), and V _n (n = 1, 2, 3, 4). An average value of the sum of products and the sum of products calculated using V _n (n = 1, 2, 3, 4, 5) can also be used as J. By doing so, the distance between the nodes can be calculated with higher accuracy. The reason for improved accuracy and gradually increasing the number of eigenvalues using sequential, the value of J shown in the above formulas, from component showing a connection state between two nodes in exponentiation A ^k of the adjacency matrix A, to alternate between high and low values, by taking the average value is more accurate to become closer to the component of the a ^k.

  Although the embodiments related to the disclosed apparatus have been described above, the present invention may be implemented in various different forms other than the above-described embodiments. Therefore, another embodiment included in the present invention will be described below.

  For example, all or some of the processes described as being automatically performed among the processes described in the embodiments may be performed manually. In addition, among the processes described in the embodiments, all or a part of the processes described as being manually performed can be automatically performed by a known method.

  In addition, the processing at each step of each processing described in each embodiment can be arbitrarily finely divided or combined according to various loads and usage conditions. Also, the steps can be omitted.

  Further, the order of processing at each step of each processing described in each embodiment can be changed according to various loads and usage conditions.

  Further, each component of each illustrated apparatus is functionally conceptual, and does not necessarily need to be physically configured as illustrated. In other words, the specific state of distribution / integration of each device is not limited to the one shown in the figure, and all or a part thereof may be functionally or physically distributed or arbitrarily distributed in arbitrary units according to various loads or usage conditions. Can be integrated and configured.

[Calculation program]
In addition, the various processes of the calculation device 10, 20 or 30 described in the above embodiment can be realized by executing a program prepared in advance on a computer system such as a personal computer or a workstation. Therefore, in the following, an example of a computer that executes a calculation program having the same function as that of the calculation device 10, 20 or 30 described in the above embodiment will be described with reference to FIG. FIG. 19 is a diagram illustrating a computer that executes a calculation program.

  As illustrated in FIG. 19, the computer 300 includes a central processing unit (CPU) 310, a read only memory (ROM) 320, a hard disk drive (HDD) 330, and a random access memory (RAM) 340. The CPU 310, the ROM 320, the HDD 330, and the RAM 340 are connected to each other via a bus 350.

  The ROM 320 stores basic programs such as an OS. Further, the HDD 330 has a calculation program 330a that exhibits the same functions as the acquisition unit, selection unit, first calculation unit, second calculation unit, third calculation unit, output control unit, and the like described in the above embodiment. Is stored in advance. Note that the calculation program 330a may be separated as appropriate. The HDD 330 is provided with distance information, adjacency matrix data, eigenvalue data, eigenvector data, and the like. These distance information, adjacency matrix data, eigenvalue data, and eigenvector data correspond to the above-described distance information 14a, adjacency matrix data 14b, eigenvalue data 24a, and eigenvector data 24b.

  Then, the CPU 310 reads the calculation program 330a from the HDD 330 and executes it.

  The CPU 310 reads out distance information, adjacency matrix data, eigenvalue data, eigenvector data, and the like and stores them in the RAM 340. Further, the CPU 310 executes the calculation program 330a using distance information, adjacency matrix data, eigenvalue data, eigenvector data, and the like stored in the RAM 340. Note that all data stored in the RAM 340 may not always be stored in the RAM 340. Data used for processing may be stored in the RAM 340.

  Note that the above-described calculation program 330a is not necessarily stored in the HDD 330 from the beginning.

  For example, the program is stored in a “portable physical medium” such as a flexible disk (FD), a CD-ROM, a DVD disk, a magneto-optical disk, or an IC card inserted into the computer 300. Then, the computer 300 may read and execute the program from these.

  Furthermore, the program is stored in “another computer (or server)” connected to the computer 300 via a public line, the Internet, a LAN, a WAN, or the like. Then, the computer 300 may read and execute the program from these.

DESCRIPTION OF SYMBOLS 10 Calculation apparatus 11 Input part 12 Output part 14 Storage part 14a Adjacency matrix data 14b Distance information 15 Control part 15b Selection part 15c First calculation part 15d Second calculation part 15e Third calculation part

Claims (13)

A selection unit that selects a plurality of groups each having a plurality of nodes from the plurality of nodes based on information indicating a connection state between the nodes in the graph having a plurality of nodes;
A first calculation unit that calculates an average distance between nodes in the group for each of the plurality of groups selected by the selection unit;
Based on the average distance between the nodes in the group calculated for each group by the first calculation unit, and information indicating the connection state between the nodes, each of the groups, and each of the plurality of nodes, A second calculation unit for calculating the distance of
Based on the distance calculated by the second calculation unit, a third calculation unit for calculating a distance between two nodes to be calculated;
A calculation device comprising: The third calculation unit calculates, for each group, a sum of distances between the two nodes calculated by the second calculation unit and the group, and among the calculated sums of distances, a minimum sum is calculated. The calculation device according to claim 1, wherein: is calculated as a distance between the two nodes. The selection unit selects a plurality of nodes satisfying a first condition from a plurality of nodes based on information indicating a connection state between the nodes, and sets a second condition for each of the selected plurality of nodes. The calculation device according to claim 1 or 2, wherein a group to be satisfied is selected.   The selection unit calculates a plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues from a matrix indicating a connection state between the nodes, and based on the calculated plurality of eigenvalues and a plurality of eigenvectors. The calculation device according to claim 1, wherein the plurality of groups are selected. A plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues are calculated from a matrix indicating a connection state between nodes in a graph having a plurality of nodes, and the calculated eigenvalues and a plurality of eigenvectors are calculated. A selection unit for selecting a plurality of groups each having a plurality of nodes, and
A first calculation unit for calculating a distance between each of the plurality of groups and each of the plurality of nodes based on the eigenvalue and the eigenvector;
Based on the distance calculated by the first calculation unit, a second calculation unit that calculates a distance between two nodes to be calculated;
A calculation device comprising: The selection unit selects, as a group, a node having an absolute value of a component of an eigenvector larger than the inverse of the square of the absolute value of the eigenvalue for each eigenvalue based on the plurality of eigenvalues and a plurality of eigenvectors. The calculation device according to claim 4, wherein: A first calculation unit that calculates a plurality of eigenvalues from a matrix indicating a connection state between nodes in a graph having a plurality of nodes, and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues;
For each of the plurality of eigenvectors, a product of a product of two components of the eigenvector corresponding to each of the two nodes whose distance is to be calculated and a k-th power value of the eigenvalue corresponding to the eigenvector is calculated. The sum of the products calculated for each eigenvector is calculated, and the calculated sum is a minimum value of k exceeding a value obtained by subtracting a predetermined value from a value indicating that the nodes are connected in the matrix. A second calculation unit that calculates the distance between the two nodes;
A calculation device comprising: On the computer,
Based on information indicating a connection state between nodes in a graph having a plurality of nodes, a plurality of groups each having a plurality of nodes are selected from the plurality of nodes,
For each of the selected groups, calculate an average distance between nodes in the group;
Based on the average distance between the nodes in the group calculated for each group, and information indicating the connection state between the nodes, to calculate the distance between each of the groups and each of the plurality of nodes,
Based on the calculated distance, a distance between two nodes to be calculated is calculated.
A calculation program for executing each process. On the computer,
A plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues are calculated from a matrix indicating a connection state between nodes in a graph having a plurality of nodes, and the calculated eigenvalues and a plurality of eigenvectors are calculated. Select multiple groups, each with multiple nodes,
Calculating a distance between each of the plurality of groups and each of the plurality of nodes based on the eigenvalue and the eigenvector;
Based on the calculated distance, calculate the distance between the two nodes of the distance calculation target,
A calculation program for executing each process. On the computer,
Calculating a plurality of eigenvalues from a matrix indicating a connection state between nodes in a graph having a plurality of nodes, and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues;
For each of the plurality of eigenvectors, a product of a product of two components of the eigenvector corresponding to each of the two nodes whose distance is to be calculated and a k-th power value of the eigenvalue corresponding to the eigenvector is calculated. The sum of the products calculated for each eigenvector is calculated, and the calculated sum is a minimum value of k exceeding a value obtained by subtracting a predetermined value from a value indicating that the nodes are connected in the matrix. Calculating as the distance between the two nodes,
A calculation program for executing each process. A calculation method executed by a computer,
Based on information indicating a connection state between nodes in a graph having a plurality of nodes, a plurality of groups each having a plurality of nodes are selected from the plurality of nodes,
For each of the selected groups, calculate an average distance between nodes in the group;
Based on the average distance between the nodes in the group calculated for each group, and information indicating the connection state between the nodes, to calculate the distance between each of the groups and each of the plurality of nodes,
Based on the calculated distance, a distance between two nodes to be calculated is calculated.
A calculation method characterized by executing each process. A calculation method executed by a computer,
A plurality of eigenvalues and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues are calculated from a matrix indicating a connection state between nodes in a graph having a plurality of nodes, and the calculated eigenvalues and a plurality of eigenvectors are calculated. Select multiple groups, each with multiple nodes,
Calculating a distance between each of the plurality of groups and each of the plurality of nodes based on the eigenvalue and the eigenvector;
Based on the calculated distance, calculate the distance between the two nodes of the distance calculation target,
A calculation method characterized by executing each process. A calculation method executed by a computer,
Calculating a plurality of eigenvalues from a matrix indicating a connection state between nodes in a graph having a plurality of nodes, and a plurality of eigenvectors corresponding to each of the plurality of eigenvalues;
For each of the plurality of eigenvectors, a product of a product of two components of the eigenvector corresponding to each of the two nodes whose distance is to be calculated and a k-th power value of the eigenvalue corresponding to the eigenvector is calculated. The sum of the products calculated for each eigenvector is calculated, and the calculated sum is a minimum value of k exceeding a value obtained by subtracting a predetermined value from a value indicating that the nodes are connected in the matrix. Calculating as the distance between the two nodes,
A calculation method characterized by executing each process.

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