KR20230099120A - Method and apparatus for continuous subgraph matching using dynamic candidate space - Google Patents

Abstract

A continuous partial graph matching method and device using a dynamic candidate space are provided. Continuous partial graph matching is performed efficiently, and matching performance is improved. The continuous partial graph matching method of the present invention includes the steps of: obtaining a directed acyclic graph (DAG) with a root from a query graph; obtaining a dynamic candidate space (DCS) for continuous partial graph matching between the query graph and a data graph based on the data graph and the DAG; and searching for the continuous partial graph matching using the DCS according to the update operation of the data graph.

Description

Continuous subgraph matching method and apparatus using dynamic candidate space

The present invention relates to a continuous subgraph matching method and apparatus, and more particularly, to a continuous subgraph matching method and apparatus using a dynamic candidate space.

The contents described below are only described for the purpose of providing background information related to an embodiment of the present invention, and the contents described do not naturally constitute prior art.

The contiguous subgraph matching problem is a problem of detecting fatal patterns or events that are newly created or deleted when the graph changes due to insertion and deletion of edges, and is one of the most important problems in graph analysis.

Prior research has been actively conducted to solve the continuous subgraph matching problem. TurboFlux stores information on whether two edges can be matched for all pairs consisting of the edges of the data graph and the edges of the spanning tree made of the query graph, and searches for embeddings by reducing the search space based on this information.

However, since TurboFlux uses the spanning tree of the query graph, it cannot consider all edges of the query graph. Also, in TurboFlux, the method of updating the data structure when an edge is deleted from the data graph is much slower than the method of updating when an edge is inserted into the data graph.

The continuous subgraph matching problem can be applied to various fields such as fraud detection in financial transactions, cyber security in computer communication networks, and recommendation systems in social networks. In order for such an application system to operate effectively, a technique capable of solving the continuous subgraph matching problem more quickly is required.

On the other hand, the above-mentioned prior art is technical information that the inventor possessed for derivation of the present invention or acquired during the derivation process of the present invention, and cannot necessarily be said to be known art disclosed to the general public prior to the filing of the present invention. .

An object of the present invention is to provide a continuous subgraph matching method and apparatus using a dynamic candidate space.

An object of the present invention is to propose a dynamic candidate space, which is a data structure for efficiently performing contiguous subgraph matching, and an update algorithm for the dynamic candidate space.

The object of the present invention is not limited to the above-mentioned tasks, and other objects and advantages of the present invention not mentioned above can be understood by the following description and will be more clearly understood by the embodiments of the present invention. It will also be seen that the objects and advantages of the present invention may be realized by means of the instrumentalities and combinations indicated in the claims.

A continuous subgraph matching method between a query graph and a data graph according to an embodiment of the present invention includes obtaining a Directed Acyclic Graph (DAG) having a root from a query graph, the query graph and the query graph based on the data graph and the DAG. Acquiring a dynamic candidate space (DCS) for continuous subgraph matching between the data graphs and searching for the continuous subgraph matching using the dynamic candidate space according to an update operation of the data graph The dynamic candidate space may include a set of candidate vertices of the data graph for a vertex of the query graph, and a backward part having a vertex of the DAG corresponding to a vertex of the query graph as a root in the candidate vertex. First embedding information associated with the embedding of the DAG and second embedding information associated with the embedding of a partial DAG having a vertex of the DAG corresponding to a vertex of the query graph as a root in the candidate vertices.

An apparatus for matching a continuous partial graph between a query graph and a data graph according to an embodiment of the present invention includes a memory for storing at least one command; and a processor, wherein the at least one instruction, when executed by the processor, causes the processor to obtain a Directed Acyclic Graph (DAG) with a root from a query graph, and to obtain the query graph based on a data graph and the DAG. Acquiring a Dynamic Candidate Space (DCS) for continuous subgraph matching between the data graph and searching for the continuous subgraph matching using the dynamic candidate space according to an update operation of the data graph; , the dynamic candidate space is a set of candidate vertices of the data graph for vertices of the query graph. In the candidate vertices, first embedding information associated with embedding of a reverse partial DAG having a vertex of the DAG corresponding to a vertex of the query graph as a root, and in the candidate vertices, information of the DAG corresponding to a vertex of the query graph. Second embedding information associated with embedding of a partial DAG having a vertex as a root may be included.

Other aspects, features and advantages other than those described above will become apparent from the following drawings, claims and detailed description of the invention.

According to the embodiment, it is possible to perform contiguous subgraph matching efficiently using a dynamic candidate space (DCS).

According to the embodiment, the DCS can be efficiently updated only for the changed part without recalculating the DCS from the beginning according to the update of the data graph.

According to the embodiment, since the DCS stores information considering all edges of the query graph, embedding search can be efficiently performed by reducing the search space.

The effects of the present invention are not limited to those mentioned above, and other effects not mentioned will be clearly understood by those skilled in the art from the description below.

1 is a diagram schematically illustrating continuous partial graph matching according to an embodiment.
2A and 2B are diagrams for explaining a contiguous subgraph matching problem by way of example.
3A shows a spanning tree of the exemplary query graph, FIG. 3B shows a directed acyclic graph (DAG) of the exemplary query graph, and FIG. 3C shows a path tree of the exemplary query graph, respectively.
4 is a block diagram of a continuous partial graph matching device according to an embodiment.
5 is a schematic flowchart of a continuous partial graph matching method according to an embodiment.
6 is a flowchart of a continuous subgraph matching method using a dynamic candidate space according to an embodiment.
7A to 7C are diagrams for illustratively explaining a process of updating a dynamic candidate space according to an embodiment.
8 is a flowchart of a method for updating a dynamic candidate space according to an embodiment when an update operation is trunk insertion.
9 is a detailed flowchart of a method for updating a dynamic candidate space according to an embodiment when an update operation is trunk insertion.
10 is a detailed flowchart of a method for updating a dynamic candidate space according to an embodiment when an update operation is trunk insertion.

Hereinafter, the present invention will be described in more detail with reference to the drawings. The invention may be embodied in many different forms and is not limited to the embodiments set forth herein. In the following embodiments, parts not directly related to the description are omitted in order to clearly describe the present invention, but this does not mean that the omitted configuration is unnecessary in implementing a device or system to which the spirit of the present invention is applied. . In addition, the same reference numbers are used for the same or similar elements throughout the specification.

In the following description, terms such as first and second may be used to describe various components, but the components should not be limited by the terms, and the terms refer to one component from another. Used only for distinguishing purposes. Also, in the following description, singular expressions include plural expressions unless the context clearly indicates otherwise.

In the following description, terms such as "comprise" or "having" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, but one or more other It should be understood that it does not preclude the possibility of addition or existence of features, numbers, steps, operations, components, parts, or combinations thereof.

The present invention relates to a big data graph analysis algorithm, and more particularly, when a data graph is updated, information of a dynamic candidate space containing matching information of a query graph is quickly updated, and subgraph matching is efficiently performed using the updated information. It's about how to do it.

This is a continuous subgraph matching problem, which is one of the most important problems in graph analysis. The continuous subgraph matching problem can be applied to various fields such as fraud detection in financial transactions, cyber security in computer communication networks, and recommendation systems in social networks.

The present invention introduces a dynamic candidate space (DCS) using a directed acyclic graph (DAG) of a query graph instead of a spanning tree of a query graph. Since the DAG includes all edges of the query graph, the present invention can further reduce the search space than TurboFlux using spanning trees, and accordingly, it can quickly solve the continuous subgraph matching problem.

In addition, the present invention improves the update time by introducing a DCS update method that operates similarly in the case of trunk insertion and trunk deletion. It was confirmed that the present invention is up to thousands of times faster through performance comparison with TurboFlux through actual graph data and generated graph data frequently used in previous studies.

The present invention will be described in detail with reference to the drawings below.

1 is a diagram schematically illustrating continuous partial graph matching according to an embodiment.

A dynamic graph is a graph that changes over time according to a graph update stream including edge insertion and edge deletion. Social media streams, computer network traffic, and financial transaction networks are examples of dynamic graphs.

As the number of dynamic graphs increases, many studies on efficient dynamic graph analysis are being conducted. Among them, detecting fatal patterns or events in dynamic graphs is one of the most critical problems as a continuous subgraph matching problem.

A continuous subgraph matching problem is a data graph, given a query graph (q), an initial data graph (g ₀ ), and a data graph update stream (Δg), according to the task of the data graph update stream (Δg). The problem is to find all embeddings of the query graph (q) that are newly created or deleted in the data graph (g) whenever (g) is updated. Here, embedding is defined as in Definition 1 below.

[Definition 1]

Given a query graph q and a data graph g, the embedding M of q in g is an injective function that satisfies the following condition.

1) Vertex u of query graph q and vertex M(u) of data graph g corresponding to vertex u have the same label.

2) The edge (M(u), M(u')) corresponding to the edge (u, u') of the query graph q exists in the data graph g.

The continuous partial graph matching apparatus 100 according to the embodiment finds an embedding M of a given query graph q in a dynamic data graph g. That is, for a data graph update event (Δo _0, Δo ₁ , Δo ₂ ; Δo _i ) such as insertion or deletion of an edge according to the data graph update stream (Δg), the data graph (g _0, g ₁ , g ₂ ; g Find the embeddings (M _0, M ₁ , M ₂ ; M _i ) of the query graph (q) that are newly created or deleted in _i ).

2A and 2B are diagrams for explaining a contiguous subgraph matching problem by way of example.

2A is an exemplary query graph q, which corresponds to a pattern to be found in data graph g. Subgraph matching means finding the embedding of the query graph (q) in the data graph (g). Successive subgraph matching means finding embeddings of a query graph (q) that are newly created or deleted in a data graph (g) updated according to a data graph update stream (Δg) that includes a series of edge insertions or edge deletions. .

2B is an exemplary data graph (g), showing an initial data graph (g ₀ ) and a dynamic graph including two edge insertions.

The data graph (g) is the initial data graph (g ₀ ) and the first edge insertion (o ₁ ) and a second trunk insertion (o ₂ ). where the first edge insertion (Δo ₁ ) and a second edge insertion Δo ₂ is obtained from the data graph update stream g.

When the edge (v ₃ , v ₆ ) is inserted into the data graph (g) by the second edge insertion (Δo ₂ ), continuous subgraph matching is the embedding of the newly created query graph (q) in the data graph (g) 200 I need to find a dog.

Since the continuous subgraph matching problem needs to find an embedding by solving the subgraph matching problem, many algorithms or ideas for solving the subgraph matching problem are used to solve the continuous subgraph matching problem. Recent subgraph matching studies showing good performance are based on Ullmann's backtracking algorithm. The backtracking algorithm is an algorithm that finds an embedding by matching vertices of the query graph to vertices of the data graph, given a query graph and a data graph. As for backtracking-based algorithms, many studies such as TurboIso, CFL-Match, and DAF have been conducted.

TurboIso (Wook-Shin Han, Jinsoo Lee, and Jeong-Hoon Lee. 2013. TurboISO: Towards UltraFast and Robust Subgraph Isomorphism Search in Large Graph Databases. In Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data. 337-348. Reference) first finds the embedding of the spanning tree made from the query graph in the data graph before finding the embedding of the query graph. Based on this result, candidate spaces of the data graph that may have embeddings in the query graph are extracted, an efficient matching order is determined for each candidate space, and embeddings are found by performing backtracking.

DAF (refer to Myoungji Han, Hyunjoon Kim, Geonmo Gu, Kunsoo Park, and Wook-Shin Han. 2019. Efficient Subgraph Matching: Harmonizing Dynamic Programming, Adpative Matching Order, and Failing Set Together. In Proceedings of SIGMOD. 1429-1446.) proposed a method to solve the subgraph matching problem using a directed acyclic graph (DAG) with a root made of the query graph instead of the spanning tree of the query graph.

DAF defined a weak embedding between a data graph and a DAG made of a query graph, which is an essential condition for embedding.

의 약한 임베딩은 DAG

의 경로 트리(path tree)를 통해 정의된다. 루트를 가지는 DAG

로 만든 경로 트리의 루트에서부터 각 리프 노드까지의 경로는

의 루트에서부터 리프 노드까지의 서로 다른 경로에 대응된다. 이때, 경로 트리는 루트에서부터 리프까지 경로의 공통 접두사를 공유한다.

의 루트를 u라고 할 때, 그래프 g의 정점 v에서

의 약한 임베딩은 u가 v에 대응되는 g에서

로 만들어지는 경로 트리의 준동형(homomorphism)으로 정의된다. 준동형은 임베딩에서 단사 조건을 뺀 함수이다.DAG

The weak embedding of DAG

It is defined through the path tree of DAG with root

The path from the root of the path tree created with to each leaf node is

Corresponds to different paths from the root of the to the leaf node. In this case, the path tree shares a common prefix of the path from the root to the leaf.

Let u be the root of at the vertex v of graph g.

The weak embedding of is at g where u corresponds to v.

It is defined as a homomorphism of the path tree made by . Homologous is the function of embedding minus the injective condition.

3A shows a spanning tree of an exemplary query graph, FIG. 3B shows a directed acyclic graph (DAG) of an exemplary query graph, and FIG. 3C shows a path tree of an exemplary query DAG.

)는 도 2a의 질의 그래프(q)로부터 만들어지는 DAG의 한 예시이다. 역방향 DAG(

)는 DAG(

)에서 간선의 방향을 뒤집어서 만들어지는 DAG를 의미한다. 도 3c는 도 3b의 DAG로부터 만들어지는 경로 트리에 대한 예시이다.3A is an example of the spanning tree of the query graph (q) of FIG. 2A, and the DAG of FIG. 3B (

) is an example of a DAG created from the query graph (q) of FIG. 2a. reverse DAG(

) is DAG(

) means a DAG created by reversing the direction of the edges. 3c is an example of a route tree created from the DAG of FIG. 3b.

(도 3b)의 약한 임베딩이다. 여기서

은 u₃을 루트로 하고 u₃, u₄, u₅를 포함하는

의 부분 DAG이다. 만약 Δo₁ 간선이 삽입되면, {(u₃, v₄), (u₄', v₆), (u₅', v₇), (u₅", v-₇)}은 v₄에서

의 약한 임베딩이면서 또한 q의 임베딩이다.For example, {(u ₃ , v ₄ ), (u ₄ ', v ₆ ), (u ₅ ', v ₇ ), (u ₅ ", v- ₈ )} is the initial data graph (g in FIG. 2b) ₀ ) in v ₄

(Fig. 3b) is the weak embedding. here

is rooted at u ₃ and includes u ₃ , u ₄ , u ₅

is a part of DAG. If the Δo ₁ edge is inserted, {(u ₃ , v ₄ ), (u ₄ ', v ₆ ), (u ₅ ', v ₇ ), (u ₅ ", v- ₇ )} is at v ₄

is a weak embedding of , and also an embedding of q.

Meanwhile, in the data graph (g), all embeddings (M) of the query graph (q) are weak embeddings of the DAG made of the query graph (q), but the reverse is not true. Therefore, weak embeddings can be used for filtering as a necessary condition for embeddings (M).

For example, if we find an embedding of a query graph (q, for example, Fig. 2a) in an initial data graph (g _0. For example, Fig. 2b), in the case of TurboIso, a spanning tree q _T built from the query graph q (eg, Fig. 2b) For example, when using Fig. 3a), since there is an embedding of q _T in g ₀ , it can be seen that there is no embedding only after going through back tracking.

, 예를 들어 도 3b)를 사용하는 DAF의 경우 g₀에

의 약한 임베딩이 존재하지 않기 때문에 백트래킹 과정 없이 임베딩이 없다는 사실을 즉시 알 수 있다.On the other hand, the DAG created by q (

, for example in the case of DAF using Fig. 3b) at g ₀

Since there is no weak embedding of , it is immediately apparent that there is no embedding without a backtracking process.

TurboFlux (Kyoungmin Kim, In Seo, Wook-Shin Han, Jeong-Hoon Lee, Sungpack Hong, Hassan Chafi, Hyungyu Shin, and Geonhwa Jeong. 2018. TurboFlux: A Fast Continuous Subgraph Matching System for Streaming Graph Data. In Proceedings of the 2018 International Conference on Management of Data. 411-426.) solves the continuous subgraph matching problem by modifying the idea of the algorithm TurboIso to solve the subgraph matching problem.

TurboFlux uses an auxiliary data structure called a data-centric graph (DCG). This auxiliary data structure stores information about whether two edges can be matched for every pair of edges in the data graph and edges in the spanning tree made in the query graph. For each graph update task, information on whether the query graph embedding can be configured for the pair of data graph edges and query graph edges in the DCG is updated, and based on this information, new or deleted embeddings are found. TurboFlux solves continuous subgraph matching problems hundreds of times faster than previous algorithms.

However, since TurboFlux uses a spanning tree made from a query graph, it has a disadvantage of not considering all edges of the query graph. In addition, according to the experimental results, TurboFlux has a limitation in that the processing speed of edge deletion is much slower than the processing speed of edge insertion due to the asymmetric update process of DCG.

4 is a block diagram of a continuous partial graph matching device according to an embodiment.

The continuous partial graph matching apparatus 100 according to the embodiment includes a memory 120 and a processor 110 storing at least one command.

The processor 110, as a kind of central processing unit, may execute one or more commands stored in the memory 120 to execute the continuous partial graph matching method according to the embodiment. The processor 110 may include all types of devices capable of processing data operations by executing instructions.

The processor 110 may mean, for example, a data processing device embedded in hardware having a physically structured circuit to perform a function expressed as a code or command included in a program. As an example of such a data processing device built into hardware, a microprocessor, a central processing unit (CPU), a processor core, a multiprocessor, an application-specific integrated integrated circuit (ASIC) circuit), a field programmable gate array (FPGA), and a graphics processing unit (GPU), but is not limited thereto.

Processor 110 may include one or more processors. For example, the processor 110 may include a CPU and a GPU. For example, the processor 110 may include a plurality of GPUs. Processor 110 may include at least one core.

The memory 120 may store instructions for executing the continuous subgraph matching method according to the embodiment and intermediate data such as a dynamic candidate space. The memory 120 may store an executable program for generating and executing one or more commands implementing the continuous subgraph matching method according to the embodiment.

The processor 110 may execute the continuous partial graph matching method according to the embodiment based on programs and instructions stored in the memory 120 .

The memory 120 may include built-in memory and/or external memory, and may include volatile memory such as DRAM, SRAM, or SDRAM, one time programmable ROM (OTPROM), PROM, EPROM, EEPROM, mask ROM, flash ROM, and NAND. Non-volatile memory such as flash memory or NOR flash memory, flash drives such as SSD, compact flash (CF) card, SD card, Micro-SD card, Mini-SD card, Xd card, or memory stick; Alternatively, it may include a storage device such as a HDD. The memory 120 may include magnetic storage media or flash storage media, but is not limited thereto.

The continuous subgraph matching apparatus 100 may step-by-step execute the continuous subgraph matching method according to the embodiment.

The continuous partial graph matching apparatus 100 includes a memory 120 storing at least one instruction and a processor 110, and when the at least one instruction is executed by the processor 110, the processor 110, A directed acyclic graph (DAG) with a root is obtained from the query graph (q), and a dynamic candidate space for continuous subgraph matching between the query graph (q) and the data graph (g) based on the data graph (g) and the DAG. (Dynamic Candidate Space; DCS) may be acquired, and an embedding of a newly created or deleted query graph q may be searched for using the dynamic candidate space according to an update operation of the data graph g.

Here, the dynamic candidate space is a set of candidate vertices of the data graph (g) for vertices of the query graph (q), in the candidate vertices, a reverse sub-DAG whose root is a vertex of the DAG corresponding to the vertex of the query graph (q). First embedding information associated with the embedding of and second embedding information associated with the embedding of a partial DAG whose root is the vertex of the DAG corresponding to the vertex of the query graph q in the candidate vertices.

At least one instruction stored in the memory 120, when executed by the processor 110, causes the processor 110 to search the query graph q in a breadth first search (BFS) to obtain a DAG. while setting the direction of the edge from the first visited vertex to the next visited vertex, and determining the vertex that makes the DAG with the highest height as the root of the DAG.

At least one instruction stored in the memory 120, when executed by the processor 110, causes the processor 110 to search for a continuous subgraph matching when an update operation is an edge insertion, according to the edge insertion, the data graph ( g), update the dynamic candidate space based on the updated data graph g, and search for new embeddings of the query graph q in the data graph g.

At least one instruction stored in the memory 120, when executed by the processor 110, causes the processor 110 to search for a contiguous subgraph matching relation in the data graph g when the update operation is an edge deletion. It may be configured to search the embedding of the query graph q to be deleted, update the data graph according to edge deletion, and update the dynamic candidate space based on the updated data graph.

In one example, the set of candidate vertices is a set of vertices of the data graph g having the same label as the label of the vertex of the query graph q.

5 is a schematic flowchart of a continuous partial graph matching method according to an embodiment.

In the embodiment, the continuous subgraph matching method between the query graph q and the data graph g includes the steps of obtaining, by the processor 110, a directed acyclic graph (DAG) with a root from the query graph q ( S1), obtaining a Dynamic Candidate Space (DCS) for continuous subgraph matching between the query graph (q) and the data graph (g) based on the data graph (g) and the DAG (S2) and data A step S3 of searching for an embedding of a newly created or deleted query graph q by using a dynamic candidate space according to an update operation of the graph g may be included.

In step S1, the processor 110 may obtain a Directed Acyclic Graph (DAG) having a root from the query graph q.

To this end, in one example, step S1 is a step of setting the direction of an edge from the first visited vertex to the next visited vertex while searching the query graph q by breadth first search by the processor 110 and A step of determining a vertex creating a DAG as a root of the DAG may be included.

In step S2, the processor 110 may obtain a dynamic candidate space for continuous subgraph matching between the query graph q and the data graph g based on the data graph g and the DAG.

Here, the dynamic candidate space is a set of candidate vertices of the data graph g for the vertices of the query graph q, and embeddings of reverse sub-DAGs with the vertices of the DAG corresponding to the vertices of the query graph as the root in the candidate vertices. In the associated first embedding information and candidate vertices, second embedding information associated with an embedding of a partial DAG having a vertex of the DAG corresponding to a vertex of the query graph q as a root may be included.

In one example, the set of candidate vertices is a set of vertices of the data graph g having the same labels as the labels of the vertices of the query graph q.

In step S3, the processor 110 may search for contiguous subgraph matching using the dynamic candidate space according to the update operation of the data graph g.

Step S3 is, by the processor 110, updating the data graph g according to the insertion of the edge when the update operation is the insertion of the edge, and updating the dynamic candidate space based on the updated data graph g. and searching for an embedding of a newly created query graph q in the data graph.

Step S3 is, by the processor 110, searching for an embedding of the query graph q to be deleted in the data graph g, when the update operation is the edge deletion; data graph g according to the edge deletion; and updating the dynamic candidate space based on the updated data graph (g).

Hereinafter, a continuous subgraph matching method according to an embodiment will be described in detail.

In solving the continuous subgraph matching problem, it is important what information is stored as an intermediate result in an auxiliary data structure. Auxiliary data structures should be designed so that updating auxiliary data structures does not take too long as data graphs are updated, while containing information that helps speed up query graph search.

According to the embodiment, a method for efficiently solving the contiguous subgraph matching problem while quickly updating an auxiliary data structure by utilizing a new concept of dynamic candidate space (DCS) is proposed.

Since the DCS uses a directed acyclic graph (DAG) instead of a spanning tree of the query graph, it can consider all edges of the query graph, which increases the filtering effect and consequently speeds up the search speed. In addition, the asymmetric update process, which is a problem of TurboFlux, is solved by using an update method that can be similarly applied to both cases of edge insertion and edge deletion.

According to the embodiment, it is possible to efficiently search for embeddings by maximally filtering out a part not including a result by using DCS and dynamically determining a matching order in a part including a result.

6 is a flowchart of a continuous subgraph matching method using a dynamic candidate space according to an embodiment.

)를 획득하는 단계(S601), 획득된 DAG(

)와 초기 데이터 그래프(g-₀)로부터 초기 DCS를 획득하는 단계(S602), 데이터 그래프(g) 갱신 스트림(Δg)에 갱신 작업이 남아있는지 확인하는 단계(S603), 데이터 그래프(g) 갱신 작업이 간선 삽입인지 또는 간선 삭제인지 확인하는 단계(S604)를 포함할 수 있다.The continuous subgraph matching method according to the embodiment is a DAG with a root from the query graph (q) (

) Obtaining step (S601), the obtained DAG (

) and the initial data graph (g- ₀ ) (S602), checking whether an update task remains in the data graph (g) update stream (Δg) (S603), updating the data graph (g) It may include a step of determining whether the task is to insert a trunk line or delete a trunk line (S604).

If the update task is inserting an edge, updating by inserting an edge in the data graph (g) (S605), updating the DCS when the data graph update task is inserting an edge (S606), and updating the data graph (g) A step of searching for an embedding of the generated query graph q (S607) may be included.

If the update operation is edge deletion, searching for an embedding of the query graph (q) to be deleted from the data graph (g) (S608), updating by deleting the edge from the data graph (g) (S609), data graph It may include updating the DCS when the update task is trunk line deletion (S610).

Steps S601 and S602 correspond to steps S1 and S2, respectively, with reference to FIG. Referring to FIG. 4 , step S3 may include steps S603 to S610.

)를 획득하는 단계(S601)는 루트를 선택하는 단계와 선택된 루트로부터 너비 우선 탐색(BFS)을 통해 DAG를 생성하는 단계를 포함한다.A DAG with a root from the query graph (q) (

) is obtained (S601) includes selecting a route and generating a DAG from the selected route through Breadth First Search (BFS).

)와 초기 데이터 그래프(g₀)로부터 획득되는 초기 DCS는 초기 데이터 그래프(g₀)에서 DAG(

)의 약한 임베딩에 대한 정보와 이후 약한 임베딩에 대한 정보를 빠르게 갱신하기 위한 추가 정보들을 담고 있다. 일 예에서, DCS에 포함된 정보들은 양방향 동적 프로그래밍(하향식 동적 프로그래밍 및 상향식 동적 프로그래밍)을 통해 획득 가능하다.Acquired DAG (

) and _the initial DCS obtained from the initial data graph (g ₀ ) is the DAG (

) and additional information for quickly updating the weak embedding information. In one example, the information contained in the DCS is obtainable through bi-directional dynamic programming (top-down dynamic programming and bottom-up dynamic programming).

After acquiring the initial DCS, processing of the update task in the data graph update stream (Δg) is performed. In order to process separately when the update operation is an edge insertion operation and an edge deletion operation, for example, it is checked whether the update operation is an edge insertion operation.

If the updating task is to insert an edge into the data graph (g), the corresponding edge is first inserted into the data graph (g) to update the data graph (g). Afterwards, since the DCS may change due to the edge inserted in the data graph (g), it is updated.

At this time, the DCS update should reflect the weak embedding information of the newly created DAG in the data graph (g). In addition, additional arrays for quickly calculating weak embedding information must be updated. After updating the DCS, the newly created query graph (q) is searched for in the data graph (g) with reference to the updated DCS. Since the embedding of the newly created query graph (q) requires weak embedding of the newly created DAG in the updated DCS, the search space can be reduced using the information of the DCS.

Similarly, when the update task is to delete an edge in the data graph (g), it can be processed. First, the embedding of the query graph (q) to be deleted from the data graph (g) is first searched before the edge information is deleted from the data graph (g) and the DCS. After the embedding search, the corresponding edge is deleted from the data graph, and the weak embedding information of the DAG deleted from the data graph (g) is reflected in the DCS and updated.

)를 생성한다. 질의 그래프(q)에서 DAG를 만들 때는 너비 우선 탐색(breadth first search, BFS)으로 그래프를 탐색하면서 먼저 방문한 정점에서 이후에 방문한 정점으로 간선의 방향을 설정한다. DAG의 루트는 위의 방법대로 생성할 때 가장 높은 높이의 DAG를 만드는 정점으로 결정한다. 여기서 루트를 가지는 DAG의 높이는 루트와 다른 정점 사이의 최단 경로의 길이 중 최댓값으로 결정된다.Step S601 is a DAG having a root from the query graph q (

) to create When creating a DAG from the query graph (q), the direction of the edge is set from the vertex visited first to the vertex visited later while searching the graph with breadth first search (BFS). The root of DAG is determined as the vertex that creates the highest height DAG when created in the above method. Here, the height of a DAG having a root is determined by the maximum value of the lengths of the shortest paths between the root and other vertices.

)와 초기 데이터 그래프 (g₀)로부터 양방향 동적 프로그래밍을 통해 초기 DCS를 획득한다. DCS는 DAG의 약한 임베딩(weak embedding)을 중간 결과로 저장하고 있다. 약한 임베딩은 임베딩의 필수 조건이기 때문에 DCS에 저장된 정보는 백트래킹의 탐색 공간을 줄이는 데 도움을 준다. DCS는 다음의 정의 2와 같이 정의한다.Step S602 is the DAG generated in step S601 (

) and the initial data graph (g ₀ ) through interactive dynamic programming to obtain the initial DCS. The DCS stores the weak embedding of the DAG as an intermediate result. Since weak embedding is a necessary condition for embedding, the information stored in the DCS helps to reduce the search space for backtracking. DCS is defined as in Definition 2 below.

[Definition 2]

) 및 데이터 그래프(g)가 주어졌을 때, DCS는 다음 요소를 포함하는 자료 구조이다.The query graph (q) and the DAG created from it (

) and a data graph (g), DCS is a data structure containing the following elements.

1) For vertex u of the query graph q, the candidate set C(u) is the set of vertices of the data graph g that have the same label as u. The v in the set C(u) is written as <u,v>.

2) If there is an edge (u, u') in the query graph (q) and an edge (v, v') in the data graph (g), between <u, v> and <u', v'> There is an edge (<u, v>, <u', v'>) of At this time, if u is a parent (or descendant) of u', <u, v> is defined as a parent (or descendant) of <u', v'>.

의 약한 임베딩이 존재하면 제 1 임베딩 정보 D₁[u, v]은 1이고 존재하지 않으면 0이다.3) For vertex u of the query graph (q) and vertex v of the data graph (g), if v is a partial DAG

The first embedding information D ₁ [u, v] is 1 if there is a weak embedding of , and 0 if it does not exist.

의 약한 임베딩이 존재하면 제 2 임베딩 정보 D₂[u,v]은 1이고 그렇지 않으면 0이다.4) For vertex u of the query graph (q) and vertex v of the data graph (g), if D ₁ [u', v'] = Partial DAG in single v

The second embedding information D ₂ [u,v] is 1 if there is a weak embedding of , and 0 otherwise.

First embedding information (D ₁ ) and second embedding information (D ₂ ), which are intermediate results stored by the DCS, are weak embedding information of partial DAGs. Based on this information, candidates can be filtered out later when searching for embeddings. Since the weak embedding of the partial DAG of the query graph q is a necessary condition for the embedding of the query graph q, all mappings (u, v) of the embeddings M of the query graph q in the data graph g are D ₂ Satisfies [u, v]=1. Accordingly, when finding the embedding of the query graph q in the data graph g, only (u, v) pairs for which the second embedding information D ₂ satisfies D ₂ [u, v]=1 need only be considered.

The first embedding information (D ₁ ) and the second embedding information (D ₂ ), which are weak embedding information of the query graph (q) in the data graph (g) stored by the DCS, can be calculated through the following recursion.

과

는 다음의 재귀를 통해 계산할 수 있다. Weak embedding information of the query graph in the data graph stored by the DCS

class

can be calculated through the following recursion.

u의 모든 부모 u_p에 대해서

을 만족하는 v에 이웃한 v_p가 C(u_p)에 존재한다.

For all parents u _p of u

A v _p adjacent to v that satisfies exists in C(u _p ).

이면서 u의 모든 자식 u_c에 대해서

을 만족하는 v에 이웃한 v_c가 C(u_c)에 존재한다.

and for all children u _c of u

A v _c adjacent to v that satisfies exists in C(u _c ).

Based on the above recursion, the first embedding information (D ₁ ) and the second embedding information (D ₂ ) may be calculated through top-down dynamic programming and bottom-up dynamic programming, respectively.

Updating the data structure when an edge is inserted

Works on each update in the data graph update stream. First, it is checked whether there are any update tasks remaining in the data graph update stream, and if all update tasks have been processed, the process is terminated (step S603). If there is an update task to be processed, whether the update task is a task of inserting an edge in the data graph or a task of deleting an existing edge is determined, and the subsequent task is performed (step S604).

Next, if the data graph updating task is an insertion task, the corresponding edge is inserted into the data graph (step S605). EO whose edge to be inserted into the data graph is (v, v'), can be processed by inserting v' into the adjacency list of vertex v and inserting v into the adjacency list of vertex v'.

Next, the DCS is updated as the edge is inserted into the data graph (step S606). If step S602 is executed again with the updated data graph, the updated DCS can be obtained by calculating the DCS from scratch. However, this method is inefficient because it recalculates the parts that do not need to be updated. Therefore, the present invention uses a method of obtaining newly created edges in the DCS and calculating only the part where the values of D ₁ and D ₂ may change.

First of all, it is necessary to obtain a set of new edges (E _DCS ) that are newly created in the DCS due to edges inserted into the data graph. If the updated edge in the data graph is (v,v'), while traversing the query graph, find (u, u') edges where u has the same label as v and u' has the same label as v'(<u, The v>, <u',v'>) edge can be put into the E _DCS set. At this time, for the convenience of the next task, make <u,v> the parent of <u',v'>. For example, in FIG. 2B , when Δo ₂ is inserted, the set of newly created edges E _DCS in DCS is (<u ₂ , v ₃ >,<u ₄ ,v ₆ >) and (<u ₂ , v ₆ >, <u ₄ , v ₃ >).

The cases in which D ₁ and D ₂ values of the DCS may change due to data graph edge insertion are as follows. If the parent <u _p ,v _p > of <u,v> can affect the value of D ₁ [u,v], then (1) the value of D ₁ [u,v] is already 1 and <u When an edge is inserted between _p ,v _p > and <u,v>, (2) an edge already exists between <u _p ,v _p > and <u,v> and D ₁ [u,v] when the value changes from 0 to 1. We define <u _p ,v _p > belonging to both cases as the updated parent of <u,v>. By calculating only D ₁ of <u,v> having an updated parent, the entire D ₁ of the DCS may not be recalculated.

Similarly, D ₂ assumes that for <u c , v _c > children of < _u ,v>, (1) D ₂ [u,v] already has a value of 1, and <u _c , v _c > and <u,v> When an edge is inserted between (2) <u _c , v _c > and <u,v>, the edge already exists and the value of D ₂ [u,v] changes from 0 to 1. do. For this case, <u _c , v _c > is defined as the updated children of <u,v>.

,

,

,

를 도입하였다. 배열

와

는 D₁을 갱신하는 데 이용하고

과

는 D₂를 갱신하는 데 이용한다.

가

와 다르게 자식만이 아닌 모든 이웃에 대해서 정의되는 이유는 이후 백트래킹 과정에서 사용하기 때문이다.The present invention is arranged to update the DCS more efficiently

,

,

,

was introduced. Arrangement

and

is used to update D ₁ and

class

is used to update D ₂ .

go

Unlike , the reason why it is defined for all neighbors, not just children, is that it is used in the later backtracking process.

는 D1[u_p,v_p]=1이고 간선 (<u_p,v_p>,<u,v>)이 존재하는 u의 부모인 u_p가 가지는 후보 v_p의 개수를 저장한다. 예를 들어서, 도 7b에서 C(u₁)에 있는 v₁과 v₂가 위의 조건을 만족하기 때문에

가 된다.

D1[u _p , v _p ]=1 and stores the number of candidates v p of u _p , which is the parent of u in which the edge (<u _p ,v _p >,<u, _v >) exists. For example, since v ₁ and v ₂ in C(u ₁ ) in FIG. 7B satisfy the above condition,

becomes

는

을 만족하는 u의 부모 u_p의 개수를 저장한다. 이때,

가 성립하는 것을 알 수 있다 (

는 u의 부모의 개수).

Is

stores the number of parent u _p of u that satisfies . At this time,

It can be seen that

is the number of parents of u).

는

이고 간선

이 존재하는 u의 이웃인 u'가 가지는 후보 v'의 개수를 저장한다.

Is

and the trunk line

stores the number of candidates v' possessed by u', a neighbor of u that exists.

는

을 만족하는 u의 자식 u_c의 개수를 저장한다. 비슷하게,

가 성립한다 (

는 u의 자식의 개수).

Is

stores the number of children _uc of u that satisfy . similarly,

is established (

is the number of children of u).

A method of updating the DCS when the trunks of the E _DCS set are newly added to the DCS using the above arrangements will be described in more detail with reference to FIGS. 8 to 10 . 8 is a flowchart illustrating a method of updating a DCS when a trunk line insertion operation is performed, and FIGS. 9 and 10 are flowcharts illustrating a subroutine called by FIG. 8 that processes an updated parent and an updated child, respectively. .

Embedding search when edges are inserted

이라고 할 때 D₂[u,v]=1이고 D₂[u',v']=1인 간선에 대해서만 부분 임베딩을 구성하여 백트래킹을 진행하면 된다. Next, an embedding of a query graph newly created in the data graph is searched for using the information of the DCS (step S607). Embedding search is based on a backtracking method that extends partial embedding. Since the embedding of a newly created query graph in the data graph must include one of the edges in E _DCS , one of the edges in E _DCS is used as the start of partial embedding. In addition, since the (u,v) pair included in the embedding must satisfy D ₂ [u,v]=1, the edge in E _DCS

, it is sufficient to configure partial embedding only for the edges with D ₂ [u,v]=1 and D ₂ [u',v']=1 and perform backtracking.

의 확장 가능한 후보의 예상 크기(estimated size of extendable candidates) E(u)는 u의 이미 대응되어있는 이웃 정점 u'들에 대해서

의 최소값으로 정의된다. 이 값은 확장 가능한 후보 집합의 실제 크기의 상한값으로 확장 가능한 후보 대신에 사용된다. 매칭 순서에 의해 선택되는 정점 u는 확장 가능한 정점 중에서 E(u)값이 가장 작은 u가 된다. 확장 가능한 정점 중 하나를 선택하였다면 해당 질의 그래프의 정점이 대응될 수 있는 확장 가능한 후보들(extendable candidates)을 계산한다. 데이터 그래프의 정점 v가 질의 그래프의 정점 u의 확장 가능한 후보이려면

을 만족하고 u의 대응된 이웃들 u'에 대해서 간선

가 데이터 그래프에 존재해야 한다. u의 확장 가능한 후보들의 집합은 C_M(u)로 표기한다. C_M(u)를 계산하였으면 u를 C_M(u)에 있는 후보 중 하나에 대응시켜 부분 임베딩을 확장하고 위의 과정을 반복하여 임베딩을 찾는다.After constructing the partial embedding with the edges in the E _DCS , repeat the following process until the embedding is found. First, one vertex is selected according to a matching order among extendable vertices of the query graph. Here, an expandable vertex means a vertex that has not yet been included in the embedding and has at least one of its neighbors mapped. scalable vertices

The estimated size of extendable candidates E(u) for u's already mapped neighboring vertices u'

is defined as the minimum value of This value is the upper limit of the actual size of the scalable candidate set, and is used instead of the scalable candidate. The vertex u selected by the matching sequence becomes u with the smallest E(u) value among vertices that can be extended. If one of the extendable vertices is selected, extendable candidates to which the vertex of the query graph can correspond are calculated. For vertex v of the data graph to be a scalable candidate for vertex u of the query graph

and for u's corresponding neighbors u' the edge

must exist in the data graph. The set of extensible candidates for u is denoted by C _M (u). After calculating C _M (u), u is matched to one of the candidates in C _M (u) to extend the partial embedding and repeat the above process to find the embedding.

Embedding navigation if edges are deleted

Even when the update operation is not to insert but to delete a trunk, it can be similar to the insertion of a trunk (steps S608 to S610). In the case of an edge deletion task, the embedding of the query graph to be deleted in the data graph is first searched before updating the data graph and the DCS (step S608). The reason why the embedding is searched first before updating the data structure is that if the data structure is updated first, the information on the deleted edge is removed and the desired embedding cannot be found. The embedding search method is the same as that of step S607.

Update data structure when edge is deleted

Next, an edge to be deleted is found in the data graph and the corresponding edge is deleted (step S609). When the edge to be deleted is (v,v'), find v' in the adjacency list of vertex v and delete it, and find v in the adjacency list of vertex v' and delete it.

Next, the DCS is updated in consideration of the edge set E _DCS deleted from the DCS (step S610). The DCS update operation (step S610) in case of trunk line deletion may be performed by slightly modifying the DCS update operation (step S606) in case of trunk line insertion. Similar to step S606, only parts where the values of D ₁ and D ₂ can be changed are calculated by reflecting the edges deleted from the DCS and through the concept of an updated parent and an updated child. The difference is that in step S610, if the parent <u _p ,v _p > of <u,v> is the updated parent of <u,v>, (1) the value of D ₁ [u _p ,v _p ] is 1 and <u If the edge between _p ,v _p > and <u,v> is deleted, or (2) the edge between <u _p ,v _p > and <u,v> exists and D ₁ [u _p ,v _p ] is changed from 1 to 0. Similarly, if a child <u _c ,v _c > of <u,v> is an updated child of <u,v>, then (1) the value of D ₂ [u _c ,v _c ] is 1 and <u _c ,v If the edge between _c > and <u,v> is deleted, or (2) the edge between <u _c ,v _c > and <u,v> exists and the value of D ₂ [u _c ,v _c ] is changed from 1 to 0. Another difference is that if the value of D ₂ [u,v] is 1 and the value of D ₁ [u,v] is changed from 1 to 0 during the update process, the value of D ₂ [u,v] is also changed according to the definition. should be changed to 0. Step S610 may be processed in a flowchart similar to that of FIGS. 8, 9, and 10 in consideration of the above points.

7A to 7C are diagrams for illustratively explaining a process of updating a dynamic candidate space according to an embodiment.

)로 만들어지는 예시적인 초기 DCS이다. 도 7b와 도 7c는 각각 제 1 간선 삽입(Δo₁) 및 제 2 간선 삽입(Δo₂) 후에 갱신된 동적 후보 공간(DCS)을 도시한다.7a, 7b, and 7c exemplarily show a dynamic candidate space (DCS) created by the dynamic graph (g) of FIG. 2b and the DAG of FIG. 3b. 7a shows the initial data graph g _-0 of FIG. 2b and the DAG of FIG. 3b (

) is an exemplary initial DCS made of 7b and 7c show first trunk insertion (Δo ₁ ), respectively. and the updated dynamic candidate space (DCS) after the second edge insertion (Δo ₂ ).

The dotted line shown in FIG. 7B indicates a newly created trunk line in the DCS due to the first trunk insertion (Δo ₁ ). In this way, when one edge is inserted in the data graph, several edges may be inserted in the DCS.

의 약한 임베딩 M'={(u₂, v₃),(u₁, v₁}}이 존재하므로 제 1 임베딩 정보 D₁[u₂, v₃]은 1이 되고, v₃에

의 약한 임베딩이 존재하지 않기 때문에 제 2 임베딩 정보 D₂[u₂, v₃]은 0이 된다.Referring to the initial DCS of FIG. 7A, since the vertices of the data graph having the same label as the vertex u ₂ of the query graph are v ₃ , v ₅ , and v ₆ , C(u ₂ )={v ₃ ,v ₅ ,v ₆ } do. Also, in v ₃

Since there is a weak embedding M′={(u ₂ , v ₃ ),(u ₁ , v ₁ }} of , the first embedding information D ₁ [u ₂ , v ₃ ] becomes 1, and v ₃

Since the weak embedding of does not exist, the second embedding information D ₂ [u ₂ , v ₃ ] becomes 0.

In FIG. 7B, since there is no (u,v) pair with D ₂ [u, v]=1, according to the embodiment, it can be immediately known that there is no embedding newly generated by the first trunk insertion (Δo ₁ ) without a separate backtracking process. there is.

However, in the case of TurboFlux using the spanning tree of FIG. 3A, the first trunk line in the data graph (FIGS. 7A to 7C are diagrams for exemplarily explaining the process of updating the dynamic candidate space according to the embodiment.

)로 만들어지는 예시적인 초기 DCS이다. 도 7b와 도 7c는 각각 제 1 간선 삽입(Δo₁) 및 제 2 간선 삽입(Δo₂) 후에 갱신된 동적 후보 공간(DCS)을 도시한다.7a, 7b, and 7c exemplarily show a dynamic candidate space (DCS) created by the dynamic graph (g) of FIG. 2b and the DAG of FIG. 3b. 7a shows the initial data graph g _-0 of FIG. 2b and the DAG of FIG. 3b (

) is an exemplary initial DCS made of 7b and 7c show first trunk insertion (Δo ₁ ), respectively. and the updated dynamic candidate space (DCS) after the second edge insertion (Δo ₂ ).

The dotted line shown in FIG. 7B indicates a newly created trunk line in the DCS due to the first trunk insertion (Δo ₁ ). In this way, when one edge is inserted in the data graph, several edges may be inserted in the DCS.

의 약한 임베딩 M'={(u₂, v₃),(u₁, v₁}}이 존재하므로 제 1 임베딩 정보 D₁[u₂, v₃]은 1이 되고, v₃에

의 약한 임베딩이 존재하지 않기 때문에 제 2 임베딩 정보 D₂[u₂, v₃]은 0이 된다.Referring to the initial DCS of FIG. 7A, since the vertices of the data graph having the same label as the vertex u ₂ of the query graph are v ₃ , v ₅ , and v ₆ , C(u ₂ )={v ₃ ,v ₅ ,v ₆ } do. Also, in v ₃

Since there is a weak embedding M′={(u ₂ , v ₃ ),(u ₁ , v ₁ }} of , the first embedding information D ₁ [u ₂ , v ₃ ] becomes 1, and v ₃

Since the weak embedding of does not exist, the second embedding information D ₂ [u ₂ , v ₃ ] becomes 0.

In FIG. 7B, since there is no (u,v) pair with D ₂ [u, v]=1, according to the embodiment, it can be immediately known that there is no embedding newly generated by the first trunk insertion (Δo ₁ ) without a separate backtracking process. there is.

However, in the case of TurboFlux using the spanning tree of FIG. 3A, since the data graph contains the embedding of the spanning tree including the first edge (Δo ₁ ), a backtracking process is required to know that there is no new embedding.

8 is a flowchart of a method for updating a dynamic candidate space according to an embodiment when an update operation is trunk insertion.

Referring to FIG. 8, step S606 first introduces two empty queues Q ₁ and Q ₂ (step S801). Q ₁ stores <u,v>, where the value of D ₁ [u,v] changed from 0 to 1 during the DCS update process, and these pairs become updated parents of their children. Similarly, Q ₂ stores <u,v> where the value of D ₂ [u,v] changes from 0 to 1, and these pairs become updated children of their parents.

If steps S803 to S812 are executed for each of the newly created edges (<u ₁ , v ₁ >, <u ₂ , v ₂ >) in the DCS in the E _DCS set, and processing of all edges is completed, step 800 is It ends (step S802). In this case, it is guaranteed that <u ₁ , v ₁ > is a parent of <u ₂ , v ₂ > according to the method of generating E _DCS- described above.

If there is an edge that has not yet been processed in the E _DCS , it is first checked whether <u ₁ , v ₁ > corresponds to the first case of the updated parent of <u ₂ , v ₂ > (step S803). According to the definition of E _DCS- , an edge is currently inserted between <u ₁ , v ₁ > and <u ₂ ,v ₂ >, so you only need to check if the value of D ₁ [u ₁ , v ₁ ] is 1. If the value of D ₁ [u, v] is 1 and <u ₁ , v ₁ > is an updated parent of <u ₂ , v ₂ >, step 900 is called with reference to FIG. 9 (step S804).

Conversely, as confirmed in step S803 whether <u ₁ , v ₁ > corresponds to the first case of the updated parent of < _{u 2} , v ₂ >, <u 2 , v ₂ > is the updated parent of <u ₁ , v ₁ >. It is checked whether the child corresponds to the first case (step S805). If the value of D ₂ [u ₂ , v ₂ ] is 1, the condition is satisfied and <u ₂ , v ₂ > is an updated child of <u ₁ , v ₁ >. Call (step S806).

9 is a detailed flowchart of a method for updating a dynamic candidate space according to an embodiment when an update operation is trunk insertion.

을 갱신하고 이 과정에서 D₁[u_c, v_c]의 값이 1이 되면 Q₁에 <u_c, v_c>을 삽입하여 <u_c, v_c>의 자식들 또한 갱신될 수 있도록 한다.Step 900 is called by receiving <u, v> and children <u _c , v _c > of <u, v> as inputs, where <u, v> is the updated parent of <u _c , v _c >. Step 900 is the previously defined

is updated, and in this process, when the value of D ₁ [u _c , v _c ] becomes 1, <u _c , v _c > is inserted into Q ₁ so that the children of <u _c , v _c > can also be updated. .

의 값이 0인지 비교하고(단계 S902), 0이 아니라면

의 값을 1 증가시키고 종료된다(단계 S910).Looking at Figure 9, at first

Compare whether the value of is 0 (step S902), and if not 0

The value of is increased by 1 and ends (step S910).

의 값이 0이라면

의 값이 0에서 1로 바뀌면서

정의에 따라

의 값은 1 증가한다(단계 S903).if

If the value of is 0

As the value of is changed from 0 to 1

by definition

The value of is increased by 1 (step S903).

의 값이 u_c의 부모의 수와 같은지 비교하고(단계 S904), 값이 같다면 D₁[u_c, v_c]의 값을 0에서 1로 갱신한 뒤(단계 S905), Q₁에 <u_c, v_c>을 삽입한다(단계 S906).D ₁ incremented to update [u _c , v _c ]

Compare whether the value of is equal to the number of parents of u _c (step S904), and if the values are equal, update the value of D ₁ [u _c , v _c ] from 0 to 1 (step S905), and Q ₁ < u _c , v _c > are inserted (step S906).

의 값이 u_c의 부모의 수와 다르다면

의 값을 1 증가시키고 종료된다(단계 S910). D₁[u_c, v_c]의 값이 1로 갱신됨에 따라서 D₂[u_c, v_c]의 값 또한 1로 갱신될 여지가 생기기 때문에 조건을 만족하는지 비교한다(단계 S907).if

If the value of is different from the number of parents of u _c

The value of is increased by 1 and ends (step S910). As the value of D ₁ [u _c , v _c ] is updated to 1, there is room for the value of D ₂ [u _c , v _c ] to be updated to 1, so whether the condition is satisfied is compared (step S907).

의 값을 1 증가시키고 종료된다(단계 S910).If the condition is satisfied, the value of D ₂ [u _c , v _c ] is updated to 1 (step S908) and <u _c , v _c > is inserted into Q ₂ (step S909). if the condition is not met

The value of is increased by 1 and ends (step S910).

10 is a detailed flowchart of a method for updating a dynamic candidate space according to an embodiment when an update operation is trunk insertion.

Step 1000 is similar to step 900 with reference to FIG. Step 1000 is called by receiving <u, v> and <u _p , v _p >, the parents of <u, v>, as inputs, where <u, v> are updated children of <u _p , v _p >.

을 갱신하고 이 과정에서 D₂[u_p, v_p]의 값이 1로 갱신되면 Q₂에 <u_p, v_p>을 삽입하여 <u_p, v_p>의 부모들 또한 갱신될 수 있도록 한다.Step 1000 is

and if the value of D ₂ [u _p , v _p ] is updated to 1 in this process, <u _p , v _p > is inserted into Q ₂ so that the parents of <u _p , v _p > can also be updated. do.

When the DCS update according to the first case of the updated parent and the updated child is completed, the DCS update according to the second case is performed. The second case of an updated parent is when an edge already exists between the two and the parent's D ₁ value changes from 0 to 1. Since Q ₁ contains <u, v> whose value of D ₁ is changed from 0 to 1, <u, v> in Q ₁ corresponds to the second case of the parent updated for its children. Therefore, you can proceed with updating the children of <u,v> in Q ₁ .

Steps S808 and S809 are performed with reference to FIG. 9 until <u, v> remains in Q ₁ (step S807). <u, v> at the front of Q ₁ is taken out (step S808), and the children of <u, v> and <u, v> are called and updated by calling step 900 with reference to FIG. 9 (step S809). . Due to step 900 called in step S809, a new <u, v> may be inserted into Q ₁ .

If all elements in Q ₁ have been processed through an iterative process, similarly, for Q ₂ , take out <u, v> at the front of Q ₂ until Q ₂ is empty (Step S810) (Step S811) and <u, v Step 1000 is called and processed for the parents of > and <u, v> (step S812).

의 값을 하나 증가시킨다 (단계 S813). 이는

의 정의가 모든 이웃에 대해서 정의되기 때문에 단계 1007에서 부모에 대해서만 갱신되기에 따로 처리해주는 것이다. Q₂에 있는 모든 <u, v>를 처리하였다면 단계 S802로 돌아가 E_DCS에 있는 다음 간선에 대해서 반복한다.Finally, for children <u _c , v _c > of <u, v>

The value of is increased by one (step S813). this is

Since the definition of is defined for all neighbors, it is processed separately because it is updated only for the parent in step 1007. If all <u, v> in Q ₂ have been processed, return to step S802 and repeat for the next edge in E _DCS .

Examples of dynamic graphs dealt with in the continuous subgraph matching problem include big data graphs such as social networks, computer communication networks, and financial transactions. Rapid detection of specific patterns in dynamic graphs is an important challenge in a variety of applications, including fraud detection in financial transactions, cybersecurity in computer communication networks, and recommender systems in social networks. The continuous subgraph matching problem solved by the present invention can be used to quickly detect a specific pattern in a dynamic graph.

The software developed with this technology has a high level of technological perfection, up to thousands of times faster than the latest researched TurboFlux. Software that performs fraud detection in financial transactions, cyber security in computer communication networks, and recommendation systems in social networks can be easily developed using already developed software.

The above-described method according to an embodiment of the present invention can be implemented as computer readable code in a non-transitory storage medium in which a computer program is recorded. A computer-readable non-transitory recording medium includes all types of recording devices in which data readable by a computer system is stored. Examples of computer-readable non-transitory recording media include Hard Disk Drive (HDD), Solid State Disk (SSD), Silicon Disk Drive (SDD), ROM, RAM, CD-ROM, magnetic tape, floppy disk, and optical data. storage devices, etc.

The description of the embodiments of the present invention described above is for illustrative purposes, and those skilled in the art can easily modify them into other specific forms without changing the technical spirit or essential features of the present invention. you will understand that Therefore, the embodiments described above should be understood as illustrative in all respects and not limiting. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined form.

The scope of the present invention is indicated by the following claims rather than the above detailed description, and all changes or modifications derived from the meaning and scope of the claims and equivalent concepts thereof should be construed as being included in the scope of the present invention.

100: continuous subgraph matching device
110: processor
120: memory

Claims (11)

A continuous subgraph matching method between a query graph and a data graph,
obtaining a Directed Acyclic Graph (DAG) with a root from the query graph;
obtaining a dynamic candidate space (DCS) for continuous subgraph matching between the query graph and the data graph based on the data graph and the DAG; and
Searching for the continuous subgraph matching using the dynamic candidate space according to the update operation of the data graph;
The dynamic candidate space,
a set of candidate vertices of the data graph for vertices of the query graph;
in the candidate vertex, first embedding information associated with embedding of an inverse part DAG taking as a root a vertex of the DAG corresponding to a vertex of the query graph; and
In the candidate vertex, second embedding information associated with an embedding of a partial DAG having a vertex of the DAG corresponding to a vertex of the query graph as a root,
Continuous subgraph matching method.
According to claim 1,
The step of obtaining the DAG,
setting a direction of an edge from a first visited vertex to a next visited vertex while searching the query graph using a breadth first search; and
Determining a vertex that creates a DAG with the highest height as the root of the DAG,
Continuous subgraph matching method.
According to claim 1,
When the update operation is edge insertion, the step of searching for contiguous subgraph matching,
updating the data graph according to the insertion of the trunk line;
updating the dynamic candidate space based on the updated data graph; and
Searching for an embedding of the query graph newly created in the data graph,
Continuous subgraph matching method.
According to claim 1,
When the update operation is an edge deletion, the step of searching for a contiguous subgraph matching relation,
searching for an embedding of the query graph to be deleted from the data graph;
updating the data graph according to the deletion of the trunk line; and
Updating the dynamic candidate space based on the updated data graph,
Continuous subgraph matching method.
According to claim 1,
The set of candidate vertices is a set of vertices of the data graph having the same label as the label of the vertex of the query graph.
Continuous subgraph matching method.
An apparatus for matching continuous subgraphs between a query graph and a data graph,
a memory storing at least one instruction; and
a processor, wherein the at least one instruction, when executed by the processor, causes the processor to:
Obtain a Directed Acyclic Graph (DAG) with a root from the query graph,
Acquiring a dynamic candidate space (DCS) for continuous subgraph matching between the query graph and the data graph based on the data graph and the DAG;
configured to search for the contiguous subgraph matching using the dynamic candidate space according to an update operation of the data graph;
The dynamic candidate space,
a set of candidate vertices of the data graph for vertices of the query graph;
in the candidate vertex, first embedding information associated with embedding of an inverse part DAG taking as a root a vertex of the DAG corresponding to a vertex of the query graph; and
In the candidate vertex, second embedding information associated with an embedding of a partial DAG having a vertex of the DAG corresponding to a vertex of the query graph as a root,
Continuous subgraph matching device.
According to claim 6,
The at least one instruction, when executed by the processor, causes the processor to: obtain the DAG;
While traversing the query graph with a breadth-first search, setting the direction of an edge from the first visited vertex to the next visited vertex;
Is configured to determine the vertex making the DAG of the highest height as the root of the DAG,
Continuous subgraph matching device.
According to claim 6,
The at least one instruction, when executed by the processor, causes the processor to search for the contiguous subgraph matching when the update operation is an edge insertion,
Updating the data graph according to the insertion of the edge;
Updating the dynamic candidate space based on the updated data graph;
And configured to explore embeddings of the query graph newly created in the data graph.
Continuous subgraph matching device.
According to claim 6,
The at least one command, when executed by the processor, causes the processor to search for the contiguous subgraph matching relationship when the update operation is an edge deletion,
Search for an embedding of the query graph to be deleted from the data graph;
Updating the data graph according to the deletion of the edge;
configured to update the dynamic candidate space based on the updated data graph;
Continuous subgraph matching device.
According to claim 6,
The set of candidate vertices is a set of vertices of the data graph having the same label as the label of the vertex of the query graph.
Continuous subgraph matching device.
A computer readable non-transitory recording medium storing a computer program including at least one instruction for executing the continuous subgraph matching method according to any one of claims 1 to 5 by a processor.

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