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DAM
2008

Minimum cost homomorphisms to semicomplete multipartite digraphs

8 years 8 months ago
Minimum cost homomorphisms to semicomplete multipartite digraphs
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). For a fixed directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by a real-world problem in defence logistics and was introduced very recently by the authors and M. Tso. Suppose we are given a pair of digraphs D, H and a positive integral cost ci(u) for each u V (D) and i V (H). The cost of a homomorphism f of D to H is uV (D) cf(u)(u). Let H be a fixed digraph. The minimum cost homomorphism problem for H, MinHOMP(H), is stated as follows: For input digraph D and costs ci(u) for each u V (D) and i V (H), verify whether there is a homomorphism of D to H and, if it does exist, find such a homomorphism of minimum cost. In our previous paper we obtained a dichotomy ...
Gregory Gutin, Arash Rafiey, Anders Yeo
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DAM
Authors Gregory Gutin, Arash Rafiey, Anders Yeo
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