Graph Pattern Matching Problem Research Articles

Continuous matching of evolving patterns over dynamic graph data

Nowadays, the scale of various graphs soars rapidly, which imposes a serious challenge to develop processing and analytic algorithms. Among them, graph pattern matching is the one of the most primitive tasks that find a wide spectrum of applications, the performance of which is yet often affected by the size and dynamicity of graphs. In order to handle large dynamic graphs, incremental pattern matching is proposed to avoid re-computing matches of patterns over the entire data graph, hence reducing the matching time and improving the overall execution performance. Due to the complexity of the problem, little work has been reported so far to solve the problem, and most of them only solve the graph pattern matching problem under the scenario of the data graph varying alone. In this article, we are devoted to a more complicated but very practical graph pattern matching problem, continuous matching of evolving patterns over dynamic graph data, and the investigation presents a novel algorithm CEPDG for continuously pattern matching along with changes of both pattern graph and data graph. Specifically, we propose a concise representation TreeMat of partial matching solutions, which can help to avoid re-computing matches of the pattern and speed up subsequent matching process. In order to enable the updates of data graph and pattern graph, we propose an incremental maintenance strategy, to efficiently maintain the intermediate results. Moreover, we conceive an effective model for estimating step-wise cost of pattern evaluation to drive the matching process. Extensive experiments verify the superiority of CEPDG.

Strong Social Graph Based Trust-Oriented Graph Pattern Matching With Multiple Constraints

Online social network is popular and graph pattern matching (GPM) has been significant in many social network based applications, such as experts finding and social position detection. However, the existing GPM methods do not consider the multiple constraints of the social contexts in GPM, which are commonly found in various applications, or they do not consider the changes of graph structure in the index maintenance of GPM, leading to low efficiency. In this paper, we first propose a multi-constrained simulation based on the bounded graph simulation, and propose a multi-constrained graph pattern matching (MC-GPM) problem. To improve the efficiency of MC-GPM in large social graphs, we propose a new concept, strong social graph (SSG), that contains the users who have strong social connections. Then, we propose an SSG-index method to index the reachability, the graph patterns, and the social contexts of social graphs. Finally, we propose an incremental algorithm to maintain the SSG-index, which can greatly save the execution time when faced with the change of the structures of SSGs. Moreover, by combining SSG-index, we develop a heuristic algorithm, called SSG-MGPM, to identify MC-GPM results effectively and efficiently. An empirical study over five real-world social graphs has demonstrated the superiority of our approach in terms of efficiency and effectiveness.

INSiGHT: A system to detect violent extremist radicalization trajectories in dynamic graphs

The number and lethality of violent extremist plots motivated by the Salafi-jihadist ideology have been growing for nearly the last decade in many parts of the world including both the U.S and Western Europe. While detecting the radicalization of violent extremists is a key component in preventing future terrorist attacks, it remains a significant challenge to law enforcement due to the issues of both scale and dynamics. We propose the development of a radicalization trend detection system as a risk assessment assistance technology that relies on data mined from public data and government databases for individuals who exhibit risk indicators for extremist violence, and enables law enforcement to monitor those individuals at the scope and scale that is lawful, and accounts for the dynamic indicative behaviors of the individuals and their associates rigorously and automatically. We frame our approach to monitoring the radicalization pattern of behaviors as a unique dynamic graph pattern matching problem, and develop a technology called INSiGHT (Investigative Search for Graph-Trajectories) to help identify individuals or small groups with conforming subgraphs to a radicalization query pattern, and follow the match trajectories over time. This paper presents the overall INSiGHT architecture and is aimed at assisting law enforcement and intelligence agencies in monitoring and screening for those individuals whose behaviors indicate a significant risk for violence, and allow for the better prioritization of limited investigative resources. We demonstrated the performance of INSiGHT on a variety of datasets, to include small synthetic radicalization-specific datasets and a real behavioral dataset of time-stamped radicalization indicators of recent U.S. violent extremists.

GStar: an efficient framework for answering top-k star queries on billion-node knowledge graphs

Massive knowledge graphs, such as Linked Open Data or Freebase, contain billions of labeled entities and relationships. Star queries aim to identify an entity given a set of related entities, and they are common with massive knowledge graphs. It is important to find the best way to answer star queries, and we can do this by treating it as a graph pattern-matching problem. Because knowledge graphs are noisy and incomplete in nature, we must find answers that match the star pattern closely, and extract a precise match if possible. Thus, here we propose GStar, a framework to identify the top-k best answers for a star query. GStar effectively and efficiently answers top-k star queries on billion-node graphs through a novel query model, an index-free query algorithm, and a distributed query system. We evaluate GStar through experiments on real-world knowledge graphs. Experimental results show that our query model effectively answers real-life star-pattern queries; our query algorithm can answer top-k queries in a near-real-time manner without requiring expensive graph indices; and the distributed system scales well with both the graph size and number of machines used for computation.

MCS-GPM: Multi-Constrained Simulation Based Graph Pattern Matching in Contextual Social Graphs

Graph Pattern Matching (GPM) has been used in lots of areas, like biology, medical science, and physics. With the advent of Online Social Networks (OSNs), recently, GPM has been playing a significant role in social network analysis, which has been widely used in, for example, finding experts, social community mining, and social position detection. Given a query which contains a pattern graph $G_Q$ and a data graph $G_D$ , a GPM algorithm finds those subgraphs, $G_M$ , that match $G_Q$ in $G_D$ . However, the existing GPM methods do not consider the multiple end-to-end constraints of the social contexts, like social relationships, social trust, and social positions on edges in $G_Q$ , which are commonly found in various applications, such as crowdsourcing travel, social network based e-commerce, and study group selection, etc. In this paper, we first conceptually extend Bounded Simulation to Multi-Constrained Simulation (MCS) , and propose a novel NP-Complete Multi-Constrained Graph Pattern Matching (MC-GPM) problem. Then, to address the efficiency issue in large-scale MC-GPM, we propose a new concept called Strong Social Component (SSC), consisting of participants with strong social connections. We also propose an approach to identifying SSCs, and propose a novel index method and a graph compression method for SSC. Moreover, we devise a multithreading heuristic algorithm, called M-HAMC, to bidirectionally search the MC-GPM results in parallel without decompressing graphs. An extensive empirical study over five real-world large-scale social graphs has demonstrated the effectiveness and efficiency of our approach.

Finding and Counting Vertex-Colored Subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.

Efficient Pattern Matching on Graph Patterns of Bounded Treewidth

Abstract This paper deals with a problem to decide whether a given graph structure appears as a pattern in the structure of a given graph. A graph pattern is a connected graph with structured variables. A variable is an ordered list of vertices that can be replaced with a connected graph by a kind of hyperedge replacements. The graph pattern matching problem (GPMP) is the computational problem to decide whether a given graph pattern matches a given graph. In this paper, we show that GPMP is solvable in polynomial time if for a given graph pattern p, the lengths of all variables of p are 2 and the base graph of p is of bounded treewidth.

Graph Pattern Matching: A Join/Semijoin Approach

Due to rapid growth of the Internet and new scientific/technological advances, there exist many new applications that model data as graphs, because graphs have sufficient expressiveness to model complicated structures. The dominance of graphs in real-world applications demands new graph processing techniques to access large data graphs effectively and efficiently. In this paper, we study a graph pattern matching problem, which is to find all patterns in a large data graph that match a user-given graph pattern. We propose new two-step R-join (reachability join) algorithms with a filter step (R-semijoin) and a fetch step (R-join) by utilizing a new cluster-based join index with graph codes in a relational database context. We also propose two optimization approaches to further optimize sequences of R-joins/R-semijoins. The first approach is based on R-join order selection followed by R-semijoin enhancement, and the second approach is to interleave R-joins with R-semijoins. We conducted extensive performance studies, and confirm the efficiency of our proposed new approaches.

Adaptive Graph Pattern Matching for Model Transformations using Model-sensitive Search Plans

The current paper makes two contributions for the graph pattern matching problem of model transformation tools. First, model-sensitive search plan generation is proposed for pattern traversal (as an extension to traditional multiplicity and type considerations of existing tools) by estimating the expected performance of search plans on typical instance models that are available at transformation design time. Then, an adaptive approach for graph pattern matching is presented, where the optimal search plan can be selected from previously generated search plans at run-time based on statistical data collected from the current instance model under transformation.

Directed Graph Pattern Matching and Topological Embedding

Pattern matching in directed graphs is a natural extension of pattern matching in trees and has many applications to different areas. In this paper, we study several pattern matching problems in ordered labeled directed graphs. For the rooted directed graph pattern matching problem, we present an efficient algorithm which, given a pattern graphPand a target graphT, runs in time and spaceO(|EP||VT|+|ET|). It is faster than the best known method by a factor ofmin{|ET|,|EP||VT|}. This algorithm can also solve the directed graph pattern matching problem without increasing time or space complexity. Our solution to this problem outperforms the best existing method by Katzenelson, Pinter and Schenfeld by a factor ofmin{|VP||ET|,|VP||EP||VT|}. We also present an algorithm for the directed graph topological embedding problem which runs in timeO(|VP||ET|+|EP|) and spaceO(|VP||VT|+|EP|+|ET|). To our knowledge, this algorithm is the first one for this problem.