JP6005583B2 - SEARCH DEVICE, SEARCH METHOD, AND SEARCH PROGRAM - Google Patents

Description

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

  In recent years, as represented by social networks, the use of large-scale networks is progressing. And, the importance of data mining and retrieval systems for large-scale networks is increasing. The network configuration can be expressed as graph data in which a computer constituting the network is a node and a link indicating a connection between the nodes is an edge. For this reason, there is a growing interest in inquiring a graph database that handles network configuration as graph data and performing search, classification, analysis, etc. of graph nodes.

  For example, when a computer as a node is a website, there is a PageRank algorithm as an algorithm for determining the importance of a web page. The PageRank algorithm calculates the importance of a node based on a random surfer model. The random surfer model models a behavior in which a user jumps to a random page after clicking a web page link a plurality of times.

  The importance of the node by PageRank corresponds to the probability in the steady state of the random walk. In each processing step of PageRank, a link destination node is selected and moved from the current node, and jumps to a random page with a certain probability. Due to its effectiveness, PageRank is applied to various applications.

Lawrence Page, Sergey Brin, Rajeev Motwani, Terry Winograd, “The PageRank Citation Ranking: Bringing Order to the Web”, 1999

  However, the above-described conventional technique has a problem that the calculation cost of PageRank is high. In other words, in the conventional PageRank calculation, the entire graph must be used repeatedly until the scores of all the nodes converge. Therefore, for large-scale graphs, high-priority nodes are searched at high speed. I can't.

  An embodiment disclosed in the present application has been made in view of the above, and an object thereof is to obtain a search result at high speed in a node search based on PageRank.

An example of an embodiment disclosed in the present application is a graph of a computer network in which a device forming a computer network is a node and a connection between devices is an edge, and k (k is greater than the number of nodes) indicating the number of solution nodes. This is a search device that accepts and searches for (no positive integer) input and outputs k solution nodes. The search device sets 0 as an initial value, i is incremented by +1, and if i = 0, the graph is a partial graph, and if i> 0, it is based on the candidate node in the i-th iteration (i -1) A subgraph construction process for constructing a subgraph of the graph in the i-th iterative calculation is executed from a set of nodes that can reach the subgraph of the graph in the iterative calculation of the first time. The search device also calculates the probability of random walk corresponding to the subgraph. Further, the search device calculates the probability of random walk and the estimated value of the lower limit value and the estimated upper limit value of the PageRank score for all the candidate nodes in the i-th iterative calculation. Further, the search device calculates a candidate node in the (i + 1) -th iteration calculation from a candidate node in the i-th iteration calculation, and the number of elements in the candidate node set in the (i + 1) -th iteration calculation is equal to k. Output a set of candidate nodes in the (i + 1) -th iteration calculation as a solution node, and if the number of elements in the candidate node set in the (i + 1) -th iteration calculation is different from k, i The subgraph construction process is executed for the new i incremented by +1. Then, when the subgraph construction process is executed for the new i, the search device sequentially executes the above-described processes again for the new i.

  According to the embodiment disclosed in the present application, for example, a search result can be obtained at high speed in a node search based on PageRank.

FIG. 1 is a block diagram showing the configuration of the search device. FIG. 2 is a flowchart showing the search process. FIG. 3 is a diagram showing a search algorithm. FIG. 4 is a diagram illustrating an example of a computer that executes a search program.

  Hereinafter, embodiments of a search device and the like disclosed in the present application will be described with reference to the drawings. In the following embodiment, a graph of a computer network in which devices forming a computer network are nodes and connections between devices are edges is represented by k indicating the number of solution nodes (k is a positive integer not exceeding the number of nodes). When an input is received and a search is performed, a candidate node having a PageRank score of higher k is output as a solution node. The following embodiments are merely examples, and do not limit the technology disclosed by the present application.

[Definition of symbols]
The symbols used in the description of the embodiment are shown in the following table. In the description of the embodiment, the vector is expressed in bold Latin small letters, and the matrix is expressed in bold Latin capital letters.

(Overview of conventional technology and problems)
Prior to the description of the embodiments, the outline and problems of the prior art will be described. In the prior art, PageRank starts a random walk from a random node, and recursively repeats the random walk with probability s (0 <s <1) in each processing step. In the prior art, each processing step jumps to a random node with a certain probability (1-s).

をｕ番目の要素ｐ［ｕ］がノードｕのPageRankのスコアに対応する列ベクトルとする。また、Ｎをグラフのノード数とする場合に、

を全ての要素の値が１／Ｎである列ベクトルとする。また、Ｗ［ｕ，ｖ］をノードｖからノードｕへ移動する確率とする場合に、

を列要素が正規化されたグラフの隣接行列とする。各ノードのPageRankのスコアは、以下の式（１）を再帰的に収束するまで繰り返し計算を行うことで得られる。 If the set V is a node of the whole graph and the set E is a set of edges, the graph G to be queried can be expressed as G = {V, E}. here,

Is a column vector in which the u-th element p [u] corresponds to the PageRank score of the node u. If N is the number of nodes in the graph,

Is a column vector in which the values of all elements are 1 / N. When W [u, v] is a probability of moving from node v to node u,

Let be the adjacency matrix of a graph with normalized column elements. The PageRank score of each node is obtained by repeatedly calculating the following expression (1) until it converges recursively.

は

に設定される。この繰り返し計算を行う従来技術の手法は、各ノードにおけるPageRankのスコアが収束するまでおこなわれる。Ｍをグラフのエッジ数とし、Ｔを収束するまでの繰り返し計算の計算回数とすると、この繰り返し計算は、Ｏ（（Ｎ＋Ｍ）・Ｔ）の計算コストを要する。そのため、従来技術の手法は、大規模なグラフに対して高速に検索が行えないという問題がある。なお、Ｏ（＊）は、ランダウの記号である。 Here, if i = 0,

Is

Set to The conventional technique for performing this iterative calculation is performed until the PageRank score at each node converges. Assuming that M is the number of edges in the graph and T is the number of calculation times until convergence, this iterative calculation requires a calculation cost of O ((N + M) · T). For this reason, the conventional technique has a problem that a large-scale graph cannot be searched at high speed. O (*) is a Landau symbol.

[Embodiment]
(Outline of the embodiment)
Embodiment described below solves the problem of the above-mentioned prior art. In the embodiment, in order to reduce the calculation cost, the estimated value of the lower limit value and the estimated value of the upper limit value of the PageRank score are calculated. That is, the embodiment excludes unnecessary nodes and edges from the search target graph based on the estimated lower and upper limit values of the PageRank score instead of using the entire search target graph as in the conventional technique. Node search is performed by repeatedly calculating the PageRank score for the subgraph.

  In the following embodiments, first, the calculation processing method and theoretical background according to the embodiment will be described, and then the configuration and processing of the search device according to the embodiment will be described.

<Calculation processing method and theoretical background>
(Method for estimating the lower and upper limits of PageRank score)
In the embodiment, in the i (i = 0, 1, 2,..., (Non-negative integer)) iteration of the PageRank score, the lower limit value and the upper limit value of the PageRank score of the nodes included in the set of candidate nodes Calculate an estimate of the value. Below, the lower limit of the PageRank score is "Lower limit", the upper limit of the PageRank score is "Upper limit", the estimated lower limit of the PageRank score is "Lower limit estimate", and the upper limit of the PageRank score The estimated value is appropriately expressed as “estimated value of the upper limit value”, the estimated value of the lower limit value of the PageRank score, and the estimated value of the upper limit value as “estimated value” as appropriate. A method for obtaining a set of candidate nodes will be described later.

となるＮ×１の列ベクトルを

とする。 In order to calculate the upper limit value, a set R _i of nodes that can reach the set C _{i of} candidate nodes is used. Here, the fact that the node u can reach the node v means that a path from the node u to the node v exists on the graph. The u th element is the maximum weight of the edge,

N × 1 column vector

And

とする。なお、

のｕ列目の成分をｒ_ｉ［ｕ］とする。ここで、グラフの隣接行列

のｉ乗を用いて、

は

と計算できる。なお、ｉ＝０ならば、

とする。ｉ番目の繰り返し計算における下限値

と、ｉ番目の繰り返し計算における上限値

を以下のように定義する。 Also, the probability of a random walk of length i is the N × 1 column vector

And In addition,

Let the component in the u-th column of r be r _i [u]. Where the adjacency matrix of the graph

Using the i power of

Is

Can be calculated. If i = 0,

And Lower limit for i-th iteration

And the upper limit in the i th iterative calculation

Is defined as follows.

  The properties of these estimated values are shown by the following Lemma 1, Lemma 2, and Lemma 3. Note that Lemma 3 indicates that the estimated value converges in the embodiment.

  In the embodiment, candidate nodes are calculated in order to recursively search for the top k nodes, and the iterative calculation ends when the number of candidate nodes reaches k. In order to calculate the estimated value, a subgraph is calculated for the nodes included in the set of candidate nodes. Then, the candidate node is dynamically updated in the repeated calculation.

(About candidate nodes)
Below, the definition of a candidate node and a subgraph, and the property of a candidate node and a subgraph are shown. The threshold value ε _{i−1 is set} to the kth highest lower limit value in the (i−1) -th iterative calculation, and a set C _i of candidate nodes in the i-th iterative calculation is defined as follows.

The properties of the set C _i are as follows.

From Auxiliary Theorem 4, since A⊆C _i , in each iteration, the candidate node set C _i-1 to the candidate node set C _i can be calculated sequentially as follows.

Further, the set C _i (i = 0, 1, 2,...) Of candidate nodes monotonously decreases for i as follows.

(About partial graphs)
In addition, the embodiment calculates an estimated value for a candidate node using a subgraph. Here, the subgraph G _i at the i-th iteration, is defined as follows.

The following holds for the set of subgraphs G _i (i = 0, 1, 2,...).

The subgraph set G _i (i = 0, 1, 2,...) Monotonously decreases for i as follows.

(About calculation of estimated values)
In addition, the lower limit value and the upper limit value in the i-th iterative calculation are sequentially calculated as follows using a set G _i of subgraphs. A method for constructing a set G _i subgraph based on the lemma 7 will be described later.

  And the calculation cost of the calculation of the lower limit value and the upper limit value in the i-th iterative calculation according to Definition 6 is as follows.

  From the above, the following two assertions are shown as theorems.

<Configuration and processing of search device>
(Configuration of search device)
FIG. 1 is a block diagram showing the configuration of the search device. The search device 10 according to the embodiment receives a graph G used for a node search query and the number k of solution nodes as input, and the candidate node having the highest rank of PageRank when the number of candidate node elements is equal to k. Are output as solution nodes. As illustrated in FIG. 1, the search device 10 includes a subgraph construction unit 11, a random walk probability calculation unit 12, an estimated value calculation unit 13, and a candidate node calculation unit 14.

The subgraph construction unit 11 receives the graph G used for the inquiry and k indicating the number of solution nodes (k is a positive integer not exceeding the number of nodes) and i indicating the number of repeated calculations (i is a non-negative integer). The subgraph G _i is calculated and output.

G Specifically, subgraph constructing unit 11, in the case of i = 0, with respect to _{C 0} is an initial set of candidate nodes _{C i C} 0 = V, with respect to _{G 0} is the initial set of subgraphs _{G i 0} = G is set. Then, the subgraph construction unit 11 outputs the subgraph G ₀ to the random walk probability calculation unit 12.

On the other hand, if i ≠ 0, the subgraph construction unit 11 increments i by +1. With this +1 increment, the subgraph G _i calculated by the subgraph construction unit 11 becomes the subgraph G _i−1 . Then, the subgraph construction unit 11 calculates the candidate node C _i based on Expression (5) in Definition 3 and Expression (6) in Definition 4. Then, the subgraph construction unit 11 calculates a set R _i of nodes that can reach the subgraph G _i−1 from the candidate node C _i by breadth-first search based on the lemma 7. Then, the subgraph construction unit 11 calculates the subgraph G _i from the node set R _i based on the definition 5 and outputs the sub graph G _i to the random walk probability calculation unit 12.

The random walk probability calculation unit 12 receives the subgraph G _i output from the subgraph construction unit 11 and, based on the lemma 6 and definition 6, the random walk probability r _i [u] corresponding to the subgraph G _i . Is output to the estimated value calculation unit 13.

Estimated value calculating section 13, from the probability r _{i [u]} and the candidate node C _i the partial graph construction unit 11 has calculated the random walk random walk probability calculation unit 12 is output, based on the definition 6, the candidate node C _i The estimated value of the lower limit value and the upper limit value of the PageRank score are calculated for all the nodes. Then, the estimated value calculation unit 13 outputs the calculated estimated value to the candidate node calculation unit 14.

The candidate node calculation unit 14 calculates a threshold value ε _i that is the kth highest lower limit value in the i th iterative calculation from the candidate nodes C _i calculated by the subgraph construction unit 11. Then, the candidate node calculation unit 14 calculates a set C _{i + 1} of candidate nodes in the (i + 1) -th iterative calculation based on the definitions 3 and 4 and the calculated threshold value ε _i . Then, the candidate node calculation unit 14 determines whether or not the number of elements | C _{i + 1} | of the candidate node set C _{i + 1} is equal to k. If the number of elements | C _{i + 1} | is equal to k, the candidate node calculation unit 14 outputs the candidate node set C _{i + 1} as a solution node. On the other hand, when the number of elements | C _{i + 1} | is different from k, the candidate node calculation unit 14 causes the subgraph construction unit 11 to perform processing after the i + 1 increment processing.

(Search process)
FIG. 2 is a flowchart showing the search process. First, the subgraph construction unit 11 of the search device 10 receives an input of a graph G used for an inquiry and k indicating the number of solution nodes (k is a positive integer not exceeding the number of nodes) (step S10). Subsequently, subgraph constructing unit 11 of the retrieval device 10 is to set to zero i indicating the number of repetitive calculations, it sets C ₀ to initial set of the set V of the candidate nodes, the initial set of subgraphs of the graph G It performs initialization to set the G ₀ (step S12).

  Subsequently, the subgraph construction unit 11 of the search device 10 determines whether i ≠ 0 (step S13). The subgraph construction unit 11 of the search device 10 moves the process to step S14 when i ≠ 0 (step S13 Yes). On the other hand, when i = 0 (No in step S13), the subgraph building unit 11 of the search device 10 moves the process to step S17.

In step S14, the subgraph construction unit 11 of the search device 10 increments i by +1. Subsequently, the subgraph construction unit 11 of the search device 10 calculates the candidate node C _i based on the expression (5) of the definition 3 and the expression (6) of the definition 4, and performs the breadth-first search based on the auxiliary theorem 7. Then, a set R _i of nodes that can reach the subgraph G _i−1 from the candidate node C _i is calculated (step S15). Subsequently, the subgraph construction unit 11 of the search device 10 calculates the subgraph G _i from the node set R _i based on the definition 5 (step S16).

Subsequently, the random walk probability calculation unit 12 of the search device 10 calculates a random walk probability r _i [u] corresponding to the subgraph G _i based on the lemma 6 and the definition 6 (step S17).

Subsequently, the estimated value calculation unit 13 of the search device 10 calculates the PageRank score for all the nodes of the candidate nodes C _i based on the definition 6 from the random walk probability r _i [u] and the candidate nodes C _i. An estimated value of the lower limit value and an estimated value of the upper limit value are calculated (step S18).

Subsequently, the candidate node calculator 14 of the retrieval device 10, the threshold epsilon _i calculated from the candidate node C _i, Definition 3 and definitions 4, and, on the basis of the threshold epsilon _i, candidates in (i + 1) th iteration of A node set C _{i + 1} is calculated (step S19). Subsequently, the candidate node calculation unit 14 of the search device 10 determines whether or not the number of elements | C _{i + 1} | of the candidate node set C _{i + 1} is equal to k (step S20). If the number of elements | C _{i + 1} | is equal to k (Yes in step S20), the candidate node calculation unit 14 of the search device 10 moves the process to step S21. On the other hand, if the number of elements | C _{i + 1} | is different from k (No in step S20), the candidate node calculation unit 14 of the search device 10 moves the process to step S14. In step S21, the candidate node calculation unit 14 of the search device 10 outputs the candidate node C _{i + 1} as a solution node. When step S21 ends, the search device 10 ends the search process.

  According to the above search processing, it is possible to perform an ad hoc search without requiring a prior calculation in the search. Further, according to the above search processing, setting of internal parameters is not required, so that the user can easily perform a search by PageRank.

(Search algorithm)
FIG. 3 is a diagram showing a search algorithm. The search algorithm shown in FIG. 3 corresponds to the process shown in the flowchart of the search process in FIG. As shown in FIG. 3, if i = 0, the search algorithm initializes the set C ₀ and the graph G ₀ from definitions 3 and 5 as C ₀ = V and G ₀ = G, respectively (see FIG. 3). 2nd to 3rd lines). If i ≠ 0, the search algorithm calculates the set R _i from the set C _i using the breadth _- first search for the graph G _i−1 (the seventh line in FIG. 3). This is because from Lemma 7, there is a property of G _i ⊆G _i−1 with respect to the subgraph G _i . Then, the search algorithm calculates the subgraph G _i from the definition 5 using the set R _i (the eighth line in FIG. 3).

Then, the search algorithm calculates the probability of random walk for each node in the subgraph G _i (line 10 to line 12 in FIG. 3). This is because the probability of random walk is necessary to calculate the estimated value based on Lemma 6. Then, the search algorithm calculates an estimated value for the candidate node C _i (13th to 15th lines in FIG. 3), and calculates a threshold ε _i from the candidate node C _i (16th line in FIG. 3). Line).

Further, the search algorithm updates the candidate node and calculates C _{i + 1} (the 17th line in FIG. 3). In the search algorithm, if the number of elements | C _{i + 1} | of the set C _{i + 1} is equal to k, that is, if | C _{i + 1} | = k, all the nodes included in the set C _{i + 1} of candidate nodes are solution nodes from the lemma 4. is there. Therefore, the iterative calculation is aborted (line 18 in FIG. 3), and a set of candidate nodes C _{i + 1} is output as a solution node (line 19 in FIG. 3).

(Effect by embodiment)
According to the above embodiment, compared to the conventional technique, the PageRank score is calculated not from the entire graph but from the partial graph, thereby enabling high-speed search. Further, according to the above-described embodiment, it is possible to search the top k nodes with the correct PageRank score for the input parameter k (k is a natural number not exceeding the number of nodes). Moreover, according to the above embodiment, it is possible to perform an ad hoc search on an arbitrary graph without requiring a prior calculation for the search. Further, according to the above embodiment, since setting of an internal parameter is not required, the user can easily perform a search by PageRank.

(System configuration of the embodiment)
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 form of distribution and integration of each device is not limited to that 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.

  Each process performed in the search device 10 may be realized in whole or in part by a CPU (Central Processing Unit) and a program that is analyzed and executed by the CPU. Each process performed in the search device 10 may be realized as hardware by wired logic.

  In addition, among the processes described in the embodiment, all or a part of the processes described as being automatically performed can be manually performed. Alternatively, all or part of the processing described as being performed manually can be automatically performed by a known method. In addition, the above-described and illustrated processing procedures, control procedures, specific names, and information including various data and parameters can be changed as appropriate unless otherwise specified.

(About the program)
It is also possible to create a program in which processing executed by a control device such as the CPU of the search device 10 described in the embodiment is described in a language that can be executed by a computer. For example, a search program in which processing executed by the control device is described in a language that can be executed by a computer can be created. In this case, the same effect as the embodiment can be obtained by the computer executing the search program. Furthermore, the processing similar to the embodiment can be realized by recording the search program on a computer-readable recording medium, and reading and executing the search program recorded on the recording medium. Hereinafter, an example of a computer that executes a program that implements the same function as the search device 10 illustrated in FIG. 1 will be described.

  FIG. 4 is a diagram illustrating an example of a computer 1000 that executes a search program. The computer 1000 includes a memory 1010 and a CPU 1020. The computer 1000 also includes a hard disk drive interface 1030, a disk drive interface 1040, a serial port interface 1050, a video adapter 1060, and a network interface 1070. These are connected by a bus 1080.

  As shown in FIG. 4, the memory 1010 includes a ROM (Read Only Memory) 1011 and a RAM 1012. The ROM 1011 stores a boot program such as BIOS (Basic Input Output System). The hard disk drive interface 1030 is connected to the hard disk drive 1031. The disk drive interface 1040 is connected to the disk drive 1041. A removable storage medium such as a magnetic disk or an optical disk is inserted into the disk drive 1041. The serial port interface 1050 is connected to a mouse 1051 and a keyboard 1052, for example. The video adapter 1060 is connected to the display 1061, for example.

  Here, as illustrated in FIG. 4, the hard disk drive 1031 stores, for example, an OS 1091, an application program 1092, a program module 1093, and program data 1094. That is, the search program is stored in, for example, the hard disk drive 1031 as a program module in which a command to be executed by the computer 1000 is described.

  The various data described in the embodiment is stored as program data, for example, in the memory 1010 or the hard disk drive 1031. The CPU 1020 reads the program module 1093 and the program data 1094 stored in the memory 1010 and the hard disk drive 1031 to the RAM 1012 as necessary. Then, the CPU 1020 executes each procedure of the search program.

  Note that the program module 1093 and the program data 1094 related to the search program are not limited to being stored in the hard disk drive 1031. That is, the program module 1093 and the program data 1094 may be stored in a removable storage medium and read by the CPU 1020 via a disk drive or the like. The program module 1093 and the program data 1094 related to the search program may be stored in another computer connected via a network (LAN (Local Area Network), WAN (Wide Area Network), etc.). The program module 1093 and the program data 1094 may be read and executed by the CPU 1020 via the network interface 1070.

DESCRIPTION OF SYMBOLS 10 Search apparatus 11 Subgraph construction part 12 Random walk probability calculation part 13 Estimated value calculation part 14 Candidate node calculation part

Claims (3)

Accepts an input of k (k is a positive integer not exceeding the number of nodes) indicating the number of solution nodes in the computer network graph in which the devices forming the computer network are nodes and the connections between the devices are edges. A search device for searching and outputting the k solution nodes,
For i that is incremented by +1 with 0 as an initial value, if i = 0, the graph is a partial graph, and if i> 0, it is based on a candidate node in the i-th iteration (i−1). A subgraph construction unit for executing a subgraph construction process for constructing a subgraph of the graph in the i-th iterative calculation from a set of nodes that can reach the subgraph of the graph in the iterative calculation of the first time;
A random walk probability calculation unit for calculating a probability of a random walk corresponding to the subgraph constructed by the subgraph construction unit;
Random walk probability calculated by the random walk probability calculation unit and an estimated value calculation unit for calculating an estimated lower limit value and an estimated upper limit value of PageRank scores for all of the candidate nodes in the i-th iterative calculation When,
When the candidate node in the (i + 1) -th iteration calculation is calculated from the candidate node in the i-th iteration calculation, and the number of elements in the candidate node set in the (i + 1) -th iteration calculation is equal to the k When the set of candidate nodes in the (i + 1) -th iteration calculation is output as a solution node, and the number of elements of the candidate node set in the (i + 1) -th iteration calculation is different from k, the subgraph A candidate node calculation unit that causes the construction unit to execute the subgraph construction process for a new i obtained by further incrementing i by +1,
When the candidate node calculation unit causes the subgraph building unit to execute the subgraph building process for the new i, the subgraph building unit, the random walk probability calculating unit, and the estimated value for the new i A search device, wherein the calculation unit and the candidate node calculation unit sequentially execute each process again. Accepts an input of k (k is a positive integer not exceeding the number of nodes) indicating the number of solution nodes in the computer network graph in which the devices forming the computer network are nodes and the connections between the devices are edges. And a search method executed by a search device that outputs the k solution nodes,
For i that is incremented by +1 with 0 as an initial value, if i = 0, the graph is a partial graph, and if i> 0, it is based on a candidate node in the i-th iteration (i−1). A subgraph construction step of executing a subgraph construction process for constructing a subgraph of the graph in the i-th iteration calculation from a set of nodes that can reach the subgraph of the graph in the iteration computation;
A random walk probability calculation step of calculating a probability of a random walk corresponding to the subgraph constructed by the subgraph construction step;
Estimated value calculating step of calculating the estimated value of the lower limit value and the upper limit value of the PageRank score for all nodes of the candidate node in the random walk probability calculated by the random walk probability calculating step and the i-th iterative calculation When,
When the candidate node in the (i + 1) -th iteration calculation is calculated from the candidate node in the i-th iteration calculation, and the number of elements in the candidate node set in the (i + 1) -th iteration calculation is equal to the k When the set of candidate nodes in the (i + 1) -th iteration calculation is output as a solution node, and the number of elements of the candidate node set in the (i + 1) -th iteration calculation is different from k, the subgraph A candidate node calculation step of executing the subgraph construction processing for a new i obtained by further incrementing the i by +1 in the construction step;
When the candidate node calculation step causes the subgraph construction step to execute the subgraph construction processing for the new i, for the new i, the subgraph construction step, the random walk probability calculation step, and the estimated value A search method, wherein the calculation step and the candidate node calculation step sequentially execute each process again. Computer
The search program for functioning as a search device of Claim 1.

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