Filtering for Subgraph Isomorphism

A subgraph isomorphism problem consists in deciding if there exists a copy of a pattern graph in a target graph. We introduce in this paper a filtering algorithm dedicated to this problem. The main idea is to label every node with respect to its relationships with other nodes of the graph, and to define a partial order on these labels in order to express compatibility of labels for subgraph isomorphism. This partial order over labels is used to filter domains. Labelings can also be strengthened by adding information from the labels of the neighbors. Such a strengthening can be applied iteratively until a fixpoint is reached. Practical experiments illustrate that our new filtering approach is more effective on difficult instances of scale free graphs than state-of-the-art algorithms and other CP approaches.

[1]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[2]  Christine Solnon,et al.  A new filtering algorithm for the graph isomorphism problem , 2006 .

[3]  Hartmut Ehrig,et al.  Refinements of Graph Transformation Systems via Rule Expressions , 2000 .

[4]  Yves Deville,et al.  CP(Graph+Map) for Approximate Graph Matching , 2005 .

[5]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6]  Christine Solnon,et al.  A Global Constraint for Graph Isomorphism Problems , 2004, CPAIOR.

[7]  Michael Rudolf.  Utilizing Constraint Satisfaction Techniques for Efficient Graph Pattern Matching , 1998, TAGT.

[8]  Laurence A. Wolsey,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings , 2007, CPAIOR.

[9]  Peter van Beek,et al.  Principles and Practice of Constraint Programming - CP 2005, 11th International Conference, CP 2005, Sitges, Spain, October 1-5, 2005, Proceedings , 2005, CP.

[10]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[11]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[12]  Yves Deville,et al.  CP(Graph): Introducing a Graph Computation Domain in Constraint Programming , 2005, CP.

[13]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[14]  Javier Larrosa,et al.  Constraint satisfaction algorithms for graph pattern matching , 2002, Mathematical Structures in Computer Science.

[15]  Julian R. Ullmann,et al.  An Algorithm for Subgraph Isomorphism , 1976, J. ACM.

[16]  Igor L. Markov,et al.  Exploiting structure in symmetry detection for CNF , 2004, Proceedings. 41st Design Automation Conference, 2004..

[17]  Albert-László Barabási,et al.  Linked - how everything is connected to everything else and what it means for business, science, and everyday life , 2003 .

[18]  Frédéric Benhamou.  Principles and Practice of Constraint Programming - CP 2006, 12th International Conference, CP 2006, Nantes, France, September 25-29, 2006, Proceedings , 2006, CP.

[19]  Mario Vento,et al.  An Improved Algorithm for Matching Large Graphs , 2001 .

[20]  Yves Deville,et al.  Approximate Constrained Subgraph Matching , 2005, CP.