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Solving subgraph isomorphism problems with constraint programming

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Abstract

The 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 global constraint and an associated filtering algorithm to solve this problem within the context of constraint programming. The main idea of the filtering algorithm 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 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 constraint programming approaches.

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Authors and Affiliations

  1. Ecole des Mines de Nantes, 4, rue Alfred Kastler, B.P. 20722, 44307, Nantes Cedex 3, France

    Stéphane Zampelli

  2. Department of Computing Science and Engineering, University of Louvain, Place Sainte-Barbe 2, 1348, Louvain-la-Neuve, Belgium

    Yves Deville

  3. Université de Lyon, Université Lyon 1, LIRIS, CNRS UMR5205, Nautibus, 43 Bd du 11 novembre, 69622, Villeurbanne cedex, France

    Christine Solnon

Authors
  1. Stéphane Zampelli
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  2. Yves Deville
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  3. Christine Solnon
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Correspondence to Christine Solnon.

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Zampelli, S., Deville, Y. & Solnon, C. Solving subgraph isomorphism problems with constraint programming. Constraints 15, 327–353 (2010). https://doi.org/10.1007/s10601-009-9074-3

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