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Bounded Tree-Width and CSP-Related Problems

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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Abstract

We study the complexity of structurally restricted homomorphism and constraint satisfaction problems. For every class of relational structures \({\mathcal C}\), let LHom \(({\mathcal C},\_)\) be the problem of deciding whether a structure \({\bf A}\in {\mathcal C}\) has a homomorphism to a given arbitrary structure B, when each element in A is only allowed a certain subset of elements of B as its image. We prove, under a certain complexity-theoretic assumption, that this list homomorphism problem is solvable in polynomial time if and only if all structures in \({\mathcal C}\) have bounded tree-width. The result is extended to the connected list homomorphism, edge list homomorphism, minimum cost homomorphism and maximum solution problems. We also show an inapproximability result for the minimum cost homomorphism problem.

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Authors and Affiliations

  1. Department of Computer and Information Science, Linköpings Universitet, S-581 83 Linköping, Sweden

    Tommy Färnqvist & Peter Jonsson

Authors
  1. Tommy Färnqvist
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  2. Peter Jonsson
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Takeshi Tokuyama

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© 2007 Springer-Verlag Berlin Heidelberg

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Färnqvist, T., Jonsson, P. (2007). Bounded Tree-Width and CSP-Related Problems. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_55

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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