Counting homomorphisms via hypergraph-based structural restrictions

  • Authors:

  • Tommy Färnqvist

  • Affiliations:

  • Department of Computer and Information Science, Linköping University, Linköping, Sweden

  • Venue:
  • ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
  • Year:
  • 2012

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Abstract

The way in which the graph structure of the constraints influences the computational complexity of counting constraint satisfaction problems (#CSPs) is well understood for constraints of bounded arity. The situation is less clear if there is no bound on the arities. Here we initiate the systematic study of these problems and identify new classes of polynomial time solvable instances based on dynamic programming over tree decompositions, in a way generalizing well-known approaches to combinatorial optimization problems on bounded treewidth graphs, but basing the decompositions on various hypergraph width measures from the literature on plain CSPs.