TY - CHAP
T1 - Minimum cost homomorphism dichotomy for locally in-semicomplete digraphs
AU - Gupta, A.
AU - Karimi, Mehdi
AU - Kim, E. J.
AU - Rafiey, A.
PY - 2008/9/22
Y1 - 2008/9/22
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.
UR - http://www.scopus.com/inward/record.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 paper
AN - SCOPUS:51849158360
SN - 3540850961
SN - 9783540850960
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
T2 - 2nd International Conference on Combinatorial Optimization and Applications, COCOA 2008
Y2 - 21 August 2008 through 24 August 2008
ER -