Graph Pattern Matching Preserving Label-Repetition Constraints

Abstract

Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete.To lower its complexity, many extensions of graph simulation have been proposed which focus on some topological constraints of pattern graphs that can be preserved in polynomial-time over data graphs. We discuss in this paper the satisfaction of a new topological constraint, called Label-Repetition constraint. To the best of our knowledge, existing polynomial approaches fail to preserve this constraint, and moreover, one can adopt only subgraph isomorphism for this end which is cost-prohibitive. We present first a necessary and sufficient condition that a data subgraph must satisfy to preserve the Label-Repetition constraints of the pattern graph. Furthermore, we define matching based on a notion of triple simulation, an extension of graph simulation by considering the new topological constraint. We show that with this extension, graph pattern matching can be performed in polynomial-time, by providing such an algorithm. Our algorithm is sub-quadratic in the size of data graphs only, and quartic in general. We show that our results can be combined with orthogonal approaches for more expressive graph pattern matching. ACM Subject ClassificationF.2 [Analysis of algorithms and problem complexity]: Nonnumerical algorithms and problems[pattern matching] . Finding replicated web collections. In Proc. of SIGMOD, pages 355-366, 2000. 2 Gao Cong, Wenfei Fan, and Anastasios Kementsietsidis. Distributed query evaluation with performance guarantees. In Proc. of SIGMOD, pages 509-520, 2007. 3 Luigi P. Cordella, Pasquale Foggia, Carlo Sansone, and Mario Vento. A (sub)graph isomorphism algorithm for matching large graphs.

Revisited Containment for Graph Patterns

“…When considering data and patterns modeled as graphs, evaluating a graph pattern Q 2 over a data graph G by simulation [16] and all its variants [2,[11][12][13][14] yields a match result defined as a function that maps each node (resp. edge) of Q 2 to all its matches in G. Therefore, we revise the traditional definition of containment for CGPs in terms of match result as follows.…”

“…In this case, SContained returns the mapping λ and the refinement relations R + and R − (lines 9-10). Otherwise, it returns ∅ (lines [11][12]. A detailed complexity analysis of algorithm SContained is given in Appendix to complete proof of Theorem 2.…”

Attributed Graph Matching via Seeds Guiding

“…Similarly, labeled graph has attracted extensive research. The graph matching algorithm has developed from a graph with only one label per node [26] to a node can have multiple labels [27]. In order to align the two graphs, the work [28] directly constructed the label using the degree of the node, and aligned the points with larger degrees according to the label; the work [29] not only used the node's own label, but also improved the matching rate by counting the label distribution of adjacent nodes.…”