The complexity of three-element min-sol and conservative min-cost-hom

Authors:
Hannes Uppman
Affiliations:
Department of Computer and Information Science, Linköping University, Linköping, Sweden
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Year:
2013

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Abstract

Thapper and Živný [STOC'13] recently classified the complexity of VCSP for all finite-valued constraint languages. However, the complexity of VCSPs for constraint languages that are not finite-valued remains poorly understood. In this paper we study the complexity of two such VCSPs, namely Min-Cost-Hom and Min-Sol. We obtain a full classification for the complexity of Min-Sol on domains that contain at most three elements and for the complexity of conservative Min-Cost-Hom on arbitrary finite domains. Our results answer a question raised by Takhanov [STACS'10, COCOON'10].