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    Characterization of a class of graphs related to pairs of disjoint matchings
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    Keywords:
    Cograph
    Disjoint sets
    Distance-hereditary graph
    Indifference graph
    Split graph
    Factor-critical graph
    Characterization
    Block graph
    Graph factorization
    Disjoint union (topology)
    Edit distance
    Distance-hereditary graph
    Subgraph isomorphism problem
    Block graph
    Graph factorization
    Factor-critical graph
    Cograph
    Subgraph Matching is a fundamental problem in graph analysis, and is widely used in many application scenarios in biology, chemistry and social network. Given a data graph and a query graph, subgraph matching aims to compute all subgraphs of the data graph that are isomorphic to the query graph. The problem is computationally expensive as the core operation it depends on, known as subgraph isomorphism, is NP-complete. In recent years, graph is increasing extensively and it is hard to compute subgraph matching on massive graph data using existing serial algorithm. Meanwhile, there exist distributed solutions, but they are mostly limited to the case where the graphs are unlabelled. In response to this gap, we study the subgraph matching problem in the multi-core environment. From the algorithm level, we propose a multi-core parallel subgraph matching algorithm called MPMatch. From the research level, we explore the concurrent allocation of subgraph matching search space to approach load balancing. We conduct extensive empirical studies on real and synthetic graphs to demonstrate that our techniques improve the performance of serial subgraph matching algorithm via parallelization and well-developed load balancing schema.
    Subgraph isomorphism problem
    Factor-critical graph
    Graph factorization
    Distance-hereditary graph
    Graph isomorphism
    Citations (8)
    Distance-hereditary graph
    Block graph
    Factor-critical graph
    Graph factorization
    Induced subgraph
    Butterfly graph
    Subgraph query in graph set returns data graph containing query graph.When the query graph and data graph both are uncertain,this paper proposes a definition of subgraph isomorphism between uncertain graphs and a definition of α-β subgraph isomorphism matching.Expectation subgraph isomorphism between uncertain graphs is a direct extension of subgraph isomorphism between deterministic graphs on probability graph model.There are two parameters α and β which are the thresholds to restrict quality of matching between query graph and data graph.This paper elaborates features of α-β subgraph isomorphism matching in detail,analyzes the differences between it and expectation subgraph isomorphism,meanwhile proposes α-β subgraph isomorphism matching decision algorithm.
    Subgraph isomorphism problem
    Graph isomorphism
    Graph factorization
    Distance-hereditary graph
    Factor-critical graph
    Graph automorphism
    Graph homomorphism
    Graph property
    Citations (0)
    Distance-hereditary graph
    Null graph
    Factor-critical graph
    Block graph
    Graph factorization
    Graph property
    Discriminative model
    Citations (23)
    Given a query graph, subgraph matching is the process of finding all the isomorphic graphs over a large data graph. Subgraph is one of the fundamental steps of many graph-based applications including recommendation system, information retrieval, social network analysis, etc. In this paper, we investigate the problem of subgraph matching over power grid knowledge graph. Since knowledge graph is a modelled as a directed, labelled, and multiple edges graph, it brings new challenges for the subgraph matching on knowledge graph. One challenge is that subgraph matching candidate calculation complexity increases with edges increase. Another challenge is that the search space of isomorphic subgraphs for a given region is huge, which needs more system resources to prune the unpromising graph candidates. To address these challenges, we propose subgraph index to accelerate the matching processing of subgraph que-ry. We use domain-specific information to construct index of power grid knowledge and maintain a small portion of search candidates in the search space. Experimental studies on real knowledge graph and synthetic graphs demonstrate that the proposed techniques are efficient compared with counterparts.
    Subgraph isomorphism problem
    Factor-critical graph
    Graph factorization
    Distance-hereditary graph
    Block graph
    Null graph
    Subgraph isomorphism problem
    Graph factorization
    Factor-critical graph
    Graph isomorphism
    Distance-hereditary graph
    Abstract Because connectivity is such a basic concept in graph theory, extremal problems concerning the average order of the connected induced subgraphs of a graph have been of notable interest. A particularly resistant open problem is whether or not, for a connected graph of order , all of whose vertices have degree at least 3, this average is at least . It is shown in this paper that if is a connected, vertex transitive graph, then the average order of the connected induced subgraphs of is at least . The extremal graph theory problems mentioned above lead to a broader theory. The concept of a Union‐Intersection System (UIS) is introduced, being a finite set of points and a set of subsets of called blocks satisfying the following simple property for all : if , then . To generalize results on the average order of a connected induced subgraph of a graph, it is conjectured that if a UIS is, in various senses, “connected and regular,” then the average size of a block is at least half the number of points. We prove that if a union‐intersection set system is regular, completely irreducible, and nonredundant, then the average size of a block is at least half the number of points.
    Distance-hereditary graph
    Block graph
    Induced subgraph
    Graph factorization
    Factor-critical graph
    Connected component
    Citations (1)