Sigma: A Set-Cover-Based Inexact Graph Matching Algorithm

Abstract

Network querying is a growing domain with vast applications ranging from screening compounds against a database of known molecules to matching sub-networks across species. Graph indexing is a powerful method for searching a large database of graphs. Most graph indexing methods to date tackle the exact matching (isomorphism) problem, limiting their applicability to specific instances in which such matches exist. Here we provide a novel graph indexing method to cope with the more general, inexact matching problem. Our method, SIGMA, builds on approximating a variant of the set-cover problem that concerns overlapping multi-sets. We extensively test our method and compare it to a baseline method and to the state-of-the-art Grafil. We show that SIGMA outperforms both, providing higher pruning power in all the tested scenarios.

Approximating the maximum common subgraph isomorphism problem with a weighted graph

“…An important feature of this technique is that the solution does not produce an exact matching for graph isomorphism, but instead an approximate matching based on a user defined error tolerance. Another approximate index based solution for improve graph query performance has been published by Mongiovì et al [2]. Their solution removes links from the graph query based on their feature sets, and then checks for subgraph isomorphism on the reduced graph query.…”

Cloud service placement via subgraph matching

“…Given a query graph, it aims to find similar subgraphs in data graphs, where similarity is usually defined by graph edit distance [41]. To speed up query processing, substructure based indices are widely adopted, such as Grafil [41], SAPPER [45 ], and many others [19], [22], [32], [37 ].…”

SMAC: Subgraph Matching and Centrality in Huge Social Networks

“…Phase II Details: Otherwise (lines [16][17][18][19][20][21][22][23][24][25][26][27][28], certain variables in the query are uninstantiated. We use a function, PartialSubst which is just like Map except that i) the substitution path is decided by the input path and ii) it should stop at the end of path and return partial substitutions.…”

“…if doesn't exist, we create a tuple for it. We compute an upper bound for the vertex score and insert the calculated upper bound into UScr c,P Q (lines [21][22][23][24][25][26]. Line 23 uses a function UB which computes an upper bound of the number of complete substitutions that a partial substitution can be extended to.…”

“…Much work has also been done on subgraph matching in biological applications where there is interest in identifying genetic structures (query graphs) that match known genetic structures (database) [23]. Gallagher [24] provides a good introduction to problem variants and query algorithms.…”