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)). 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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Gutin, G., Rafiey, A., Yeo, A. (2008). Minimum Cost Homomorphism Dichotomy for Oriented Cycles. In: Fleischer, R., Xu, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2008. Lecture Notes in Computer Science, vol 5034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68880-8_22
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DOI: https://doi.org/10.1007/978-3-540-68880-8_22
Publisher Name: Springer, Berlin, Heidelberg
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