Approximate Graph Isomorphism

  • Vikraman Arvind
  • Johannes Köbler
  • Sebastian Kuhnert
  • Yadu Vasudev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)

Abstract

We study optimization versions of Graph Isomorphism. Given two graphs G 1,G 2, we are interested in finding a bijection π from V(G 1) to V(G 2) that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an n O(logn) time approximation scheme that for any constant factor α < 1, computes an α-approximation. We prove this by combining the n O(logn) time additive error approximation algorithm of Arora et al. [Math. Program., 92, 2002] with a simple averaging algorithm. We also consider the corresponding minimization problem (of mismatches) and prove that it is NP-hard to α-approximate for any constant factor α. Further, we show that it is also NP-hard to approximate the maximum number of edges mapped to edges beyond a factor of 0.94.

We also explore these optimization problems for bounded color class graphs which is a well studied tractable special case of Graph Isomorphism. Surprisingly, the bounded color class case turns out to be harder than the uncolored case in the approximate setting.

Keywords

Approximation Algorithm Polynomial Time Complete Bipartite Graph Quadratic Assignment Problem Graph Isomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vikraman Arvind
    • 1
  • Johannes Köbler
    • 2
  • Sebastian Kuhnert
    • 2
  • Yadu Vasudev
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Institut für InformatikHumboldt-Universität zu BerlinGermany

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