### Abstract

For digraphs G and H, a homomorphism of G to H is a mapping such that uv∈ ∈A(G) implies f(u)f(v)∈ ∈A(H). In the minimum cost homomorphism problem we associate costs c _{i} (u), u∈ ∈V(G), i∈ ∈V(H) with the mapping of u to i and the cost of a homomorphism f is defined Σ_{u∈V(G)} c _{f(u)}(u) accordingly. Here the minimum cost homomorphism problem for a fixed digraph H, denoted by MinHOM(H), is to check whether there exists a homomorphism of G to H and to obtain one of minimum cost, if one does exit. The minimum cost homomorphism problem is now well understood for digraphs with loops. For loopless digraphs only partial results are known. In this paper, we find a full dichotomy classification of MinHom(H), when H is a locally in-semicomplete digraph. This is one of the largest classes of loopless digraphs for which such dichotomy classification has been proved. This paper extends the previous result for locally semicomplete digraphs.

Original language | English |
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Title of host publication | Combinatorial Optimization and Applications - Second International Conference, COCOA 2008, Proceedings |

Pages | 374-383 |

Number of pages | 10 |

Volume | 5165 LNCS |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 2nd International Conference on Combinatorial Optimization and Applications, COCOA 2008 - St. John's, NL, Canada Duration: 21 Aug 2008 → 24 Aug 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5165 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 2nd International Conference on Combinatorial Optimization and Applications, COCOA 2008 |
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Country | Canada |

City | St. John's, NL |

Period | 21/8/08 → 24/8/08 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Optimization and Applications - Second International Conference, COCOA 2008, Proceedings*(Vol. 5165 LNCS, pp. 374-383). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5165 LNCS). https://doi.org/10.1007/978-3-540-85097-7_35

**Minimum cost homomorphism dichotomy for locally in-semicomplete digraphs.** / Gupta, A.; Karimi, M.; Kim, E. J.; Rafiey, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Combinatorial Optimization and Applications - Second International Conference, COCOA 2008, Proceedings.*vol. 5165 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5165 LNCS, pp. 374-383, 2nd International Conference on Combinatorial Optimization and Applications, COCOA 2008, St. John's, NL, Canada, 21/8/08. https://doi.org/10.1007/978-3-540-85097-7_35

}

TY - GEN

T1 - Minimum cost homomorphism dichotomy for locally in-semicomplete digraphs

AU - Gupta, A.

AU - Karimi, M.

AU - Kim, E. J.

AU - Rafiey, A.

PY - 2008

Y1 - 2008

N2 - For digraphs G and H, a homomorphism of G to H is a mapping such that uv∈ ∈A(G) implies f(u)f(v)∈ ∈A(H). In the minimum cost homomorphism problem we associate costs c i (u), u∈ ∈V(G), i∈ ∈V(H) with the mapping of u to i and the cost of a homomorphism f is defined Σu∈V(G) c f(u)(u) accordingly. Here the minimum cost homomorphism problem for a fixed digraph H, denoted by MinHOM(H), is to check whether there exists a homomorphism of G to H and to obtain one of minimum cost, if one does exit. The minimum cost homomorphism problem is now well understood for digraphs with loops. For loopless digraphs only partial results are known. In this paper, we find a full dichotomy classification of MinHom(H), when H is a locally in-semicomplete digraph. This is one of the largest classes of loopless digraphs for which such dichotomy classification has been proved. This paper extends the previous result for locally semicomplete digraphs.

AB - For digraphs G and H, a homomorphism of G to H is a mapping such that uv∈ ∈A(G) implies f(u)f(v)∈ ∈A(H). In the minimum cost homomorphism problem we associate costs c i (u), u∈ ∈V(G), i∈ ∈V(H) with the mapping of u to i and the cost of a homomorphism f is defined Σu∈V(G) c f(u)(u) accordingly. Here the minimum cost homomorphism problem for a fixed digraph H, denoted by MinHOM(H), is to check whether there exists a homomorphism of G to H and to obtain one of minimum cost, if one does exit. The minimum cost homomorphism problem is now well understood for digraphs with loops. For loopless digraphs only partial results are known. In this paper, we find a full dichotomy classification of MinHom(H), when H is a locally in-semicomplete digraph. This is one of the largest classes of loopless digraphs for which such dichotomy classification has been proved. This paper extends the previous result for locally semicomplete digraphs.

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UR - http://www.scopus.com/inward/citedby.url?scp=51849158360&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85097-7_35

DO - 10.1007/978-3-540-85097-7_35

M3 - Conference contribution

SN - 3540850961

SN - 9783540850960

VL - 5165 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 374

EP - 383

BT - Combinatorial Optimization and Applications - Second International Conference, COCOA 2008, Proceedings

ER -