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AAIM
2008
Springer

Minimum Cost Homomorphism Dichotomy for Oriented Cycles

9 years 4 months ago
Minimum Cost Homomorphism Dichotomy for Oriented Cycles
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 ci(u), i ∈ V (H), then the cost of the homomorphism f is u∈V (D) cf(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 ci(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.
Gregory Gutin, Arash Rafiey, Anders Yeo
Added 01 Jun 2010
Updated 01 Jun 2010
Type Conference
Year 2008
Where AAIM
Authors Gregory Gutin, Arash Rafiey, Anders Yeo
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