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Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

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Principles and Practice of Constraint Programming (CP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9892))

Abstract

The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

C. McCreesh was supported by the Engineering and Physical Sciences Research Council [grant number EP/K503058/1].

S.N. Ndiaye and C. Solnon were supported by the ANR project SoLStiCe (ANR-13-BS02-0002-01).

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Authors and Affiliations

  1. University of Glasgow, Glasgow, Scotland

    Ciaran McCreesh & Patrick Prosser

  2. Université Lyon 1, LIRIS, UMR5205, 69621, Villeurbanne, France

    Samba Ndojh Ndiaye

  3. INSA-Lyon, LIRIS, UMR5205, 69621, Villeurbanne, France

    Christine Solnon

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  1. Ciaran McCreesh
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  2. Samba Ndojh Ndiaye
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  3. Patrick Prosser
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  4. Christine Solnon
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Correspondence to Ciaran McCreesh .

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  1. University of Nice Sophia Antipolis , Sophia Antipolis, France

    Michel Rueher

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McCreesh, C., Ndiaye, S.N., Prosser, P., Solnon, C. (2016). Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_23

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