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Polyhedral study of the maximum common induced subgraph problem

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  • Breno Piva
  • Cid Souza

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Breno Piva & Cid Souza, 2012. "Polyhedral study of the maximum common induced subgraph problem," Annals of Operations Research, Springer, vol. 199(1), pages 77-102, October.
    • Handle: RePEc:spr:annopr:v:199:y:2012:i:1:p:77-102:10.1007/s10479-011-1019-8
    DOI: 10.1007/s10479-011-1019-8
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