Approximation of minimum cost homomorphisms

  • Authors:

  • Pavol Hell;Monaldo Mastrolilli;Mayssam Mohammadi Nevisi;Arash Rafiey

  • Affiliations:

  • School of Computing Science, SFU, Burnaby, Canada;IDSIA, Lugano, Switzerland;School of Computing Science, SFU, Burnaby, Canada;IDSIA, Lugano, Switzerland, Informatics Department, University of Bergen, Norway

  • Venue:
  • ESA'12 Proceedings of the 20th Annual European conference on Algorithms
  • Year:
  • 2012

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Abstract

Let H be a fixed graph without loops. We prove that if H is a co-circular arc bigraph then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm; otherwise the minimum cost homomorphism problem to H is known to be not approximable. This solves a problem posed in an earlier paper. For the purposes of the approximation, we provide a new characterization of co-circular arc bigraphs by the existence of min ordering. Our algorithm is then obtained by derandomizing a two-phase randomized procedure. We show a similar result for graphs H in which all vertices have loops: if H is an interval graph, then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm, and otherwise the minimum cost homomorphism problem to H is not approximable.