Minimum Cost Homomorphism Dichotomy for Oriented Cycles

  • Gregory Gutin
  • Arash Rafiey
  • Anders Yeo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)


For digraphs D and H, a mapping f: V(D) →V(H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). If, moreover, each vertex u ∈ V(D) is associated with costs c i (u), i ∈ V(H), then the cost of the homomorphism f is ∑  u ∈ V(D) c f(u)(u). For each fixed digraph H, we have the minimum cost homomorphism problem for H (abbreviated MinHOM(H)). In this discrete optimization problem, we are to decide, for an input graph D with costs c i (u), u ∈ V(D), i ∈ V(H), whether there exists a homomorphism of D to H and, if one exists, to find one of minimum cost. We obtain a dichotomy classification for the time complexity of MinHOM(H) when H is an oriented cycle. We conjecture a dichotomy classification for all digraphs with possible loops.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gregory Gutin
    • 1
  • Arash Rafiey
    • 2
  • Anders Yeo
    • 1
  1. 1.Department of Computer Science Royal HollowayUniversity of LondonEghamUK
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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