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Approximate Graph Isomorphism

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Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This work was supported by Alexander von Humboldt Foundation in its research group linkage program. The third author was supported by DFG grant KO 1053/7-1.

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Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, India

    Vikraman Arvind & Yadu Vasudev

  2. Institut für Informatik, Humboldt-Universität zu Berlin, Germany

    Johannes Köbler & Sebastian Kuhnert

Authors
  1. Vikraman Arvind
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  2. Johannes Köbler
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  3. Sebastian Kuhnert
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  4. Yadu Vasudev
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Arvind, V., Köbler, J., Kuhnert, S., Vasudev, Y. (2012). Approximate Graph Isomorphism. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_12

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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