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Polyhedral study of the maximum common induced subgraph problem

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Abstract

In this paper we present an exact algorithm for the Maximum Common Induced Subgraph Problem (MCIS) by addressing it directly, using Integer Programming (IP) and polyhedral combinatorics. We study the MCIS polytope and introduce strong valid inequalities, some of which we prove to define facets. Besides, we show an equivalence between our IP model for MCIS and a well-known formulation for the Maximum Clique problem. We report on computational results of branch-and-bound (B&B) and branch-and-cut (B&C) algorithms we implemented and compare them to those yielded by an existing combinatorial algorithm.

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Authors and Affiliations

  1. Institute of Computing, University of Campinas, Av. Albert Einstein 1251, Barão Geraldo, 13083-852, Campinas, SP, Brazil

    Breno Piva & Cid Carvalho de Souza

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  1. Breno Piva
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  2. Cid Carvalho de Souza
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Correspondence to Breno Piva.

Additional information

Financial support by Fapesp, grant number 2007/53617-4 (10/2007-02/2009) and CNPq, grants number 132034/2007-7 (03/2007-09/2007), 301732/2007-8 and 472504/2007-0.

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Piva, B., de Souza, C.C. Polyhedral study of the maximum common induced subgraph problem. Ann Oper Res 199, 77–102 (2012). https://doi.org/10.1007/s10479-011-1019-8

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