Article

Minimum Cost Homomorphism Dichotomy for Oriented Cycles.

Graphs and Combinatorics (Impact Factor: 0.35). 01/2009; 25:521-531. DOI: 10.1007/s00373-009-0853-9
Source: DBLP

ABSTRACT 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)). The problem is 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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