Minimum Cost Homomorphism Dichotomy for Locally In-Semicomplete Digraphs

  • Authors:

  • A. Gupta;M. Karimi;E. J. Kim;A. Rafiey

  • Affiliations:

  • School of Computing Science, Simon Fraser University, Burnaby, Canada V5A 1S6;School of Computing Science, Simon Fraser University, Burnaby, Canada V5A 1S6;Department of Computer Science Royal Holloway, University of London, Egham, UK TW20 0EX;School of Computing Science, Simon Fraser University, Burnaby, Canada V5A 1S6

  • Venue:
  • COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
  • Year:
  • 2008

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Abstract

For digraphs Gand H, a homomorphism of Gto His a mapping such that uv驴 A(G) implies f(u)f(v) 驴 A(H). In the minimum cost homomorphism problemwe associate costs ci(u), u驴 V(G), i驴 V(H) with the mapping of uto iand the cost of a homomorphism fis defined 驴 u驴 V(G)cf(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 Gto Hand 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 His 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.