Graphs and Combinatorics

, 25:521 | Cite as

Minimum Cost Homomorphism Dichotomy for Oriented Cycles

  • Gregory Gutin
  • Arash Rafiey
  • Anders Yeo


For digraphs D and H, a mapping f : V(D) → V(H) is a homomorphism of D to H if uvA(D) implies f(u) f(v) ∈ A(H). If, moreover, each vertex uV(D) is associated with costs c i (u), iV(H), then the cost of the homomorphism f is ∑ uV(D) c f(u)(u). For each fixed digraph H, we have the minimum cost homomorphism problem for H (abbreviated MinHOM(H)). The problem is to decide, for an input graph D with costs c i (u), uV(D), iV(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.


Directed graph Homomorphism Minimum cost Dichotomy 


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Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.Department of Computer Science Royal HollowayUniversity of LondonEghamUK
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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