English

Three-Element Min-Sol and Conservative Min-Cost-Hom

Computational Complexity 2013-10-01 v5

Abstract

Thapper and Zivny [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].

Cite

@article{arxiv.1301.0027,
  title  = {Three-Element Min-Sol and Conservative Min-Cost-Hom},
  author = {Hannes Uppman},
  journal= {arXiv preprint arXiv:1301.0027},
  year   = {2013}
}
R2 v1 2026-06-21T23:02:28.009Z