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Approximability Distance in the Space of H-Colourability Problems

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Computer Science - Theory and Applications (CSR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5675))

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Abstract

A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. We study the approximability properties of the Weighted Maximum H -Colourable Subgraph problem (Max H -Col). The instances of this problem are edge-weighted graphs G and the objective is to find a subgraph of G that has maximal total edge weight, under the condition that the subgraph has a homomorphism to H; note that for H = K k this problem is equivalent to Max k -cut. To this end, we introduce a metric structure on the space of graphs which allows us to extend previously known approximability results to larger classes of graphs. Specifically, the approximation algorithms for Max cut by Goemans and Williamson and Max k -cut by Frieze and Jerrum can be used to yield non-trivial approximation results for Max H -Col. For a variety of graphs, we show near-optimality results under the Unique Games Conjecture. We also use our method for comparing the performance of Frieze & Jerrum’s algorithm with Håstad’s approximation algorithm for general Max 2-Csp. This comparison is, in most cases, favourable to Frieze & Jerrum.

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Authors and Affiliations

  1. Department of Computer and Information Science, Linköpings universitet, SE-581 83, Linköping, Sweden

    Tommy Färnqvist, Peter Jonsson & Johan Thapper

Authors
  1. Tommy Färnqvist
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  2. Peter Jonsson
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  3. Johan Thapper
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Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Koptyug av, 630090, Novosibirsk, Russia

    Anna Frid

  2. Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090, Novosibirsk, Russia

    Andrey Morozov

  3. Max Planck Institute for Software Systems, Campus E1 4, 66123, Saarbrücken, Germany

    Andrey Rybalchenko

  4. Lehrstuhl für Theoretische Informatik, Institut für Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97974, Würzburg, Germany

    Klaus W. Wagner

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Färnqvist, T., Jonsson, P., Thapper, J. (2009). Approximability Distance in the Space of H-Colourability Problems. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_11

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  • DOI: https://doi.org/10.1007/978-3-642-03351-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03350-6

  • Online ISBN: 978-3-642-03351-3

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