Bounded tree-width and CSP-related problems

  • Authors:

  • Tommy Färnqvist;Peter Jonsson

  • Affiliations:

  • Department of Computer and Information Science, Linköpings Universitet, Linköping, Sweden;Department of Computer and Information Science, Linköpings Universitet, Linköping, Sweden

  • Venue:
  • ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
  • Year:
  • 2007

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Abstract

We study the complexity of structurally restricted homomorphism and constraint satisfaction problems. For every class of relational structures C, let LHOM(C, _) be the problem of deciding whether a structure A ∈ 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 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.