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CORR

2007

Springer

2007

Springer

For digraphs G and H, a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of a homomorphism f is u∈V (G) cf(u)(u). For each ﬁxed digraph H, the minimum cost homomorphism problem for H, denoted MinHOM(H), can be formulated as follows: Given an input digraph G, together with costs ci(u), u ∈ V (G), i ∈ V (H), decide whether there exists a homomorphism of G to H and, if one exists, to ﬁnd one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems such as the minimum cost chromatic partition and repair analysis problems. We focus on the minimum cost homomorphism problem for locally semicomplete digraphs and quasi-transitive digraphs which are two well-known generalizations of tournaments. Using graph-theoretic characterization results for the two digraph classes, we...

Related Content

Added |
13 Dec 2010 |

Updated |
13 Dec 2010 |

Type |
Journal |

Year |
2007 |

Where |
CORR |

Authors |
Arvind Gupta, Gregory Gutin, Mehdi Karimi, Eun Jung Kim, Arash Rafiey |

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