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. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Gutin, G., Rafiey, A., & Yeo, A. (2008). Minimum cost homomorphism dichotomy for oriented cycles. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5034 LNCS, pp. 224–234). https://doi.org/10.1007/978-3-540-68880-8_22
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