Computational Complexity of the Minimum Cost Homomorphism Problem on Three-element Domains
Number of Authors: 1
2014 (English)Conference paper (Refereed)
In this paper we study the computational complexity of the extended minimum cost homomorphism problem (Min-Cost-Hom) as a function of a constraint language, i.e. a set of constraint relations and cost functions that are allowed to appear in instances. A wide range of natural combinatorial optimisation problems can be expressed as extended Min-Cost-Homs and a classification of their complexity would be highly desirable, both from a direct, applied point of view as well as from a theoretical perspective.
The extended Min-Cost-Hom can be understood either as a flexible optimisation version of the constraint satisfaction problem (CSP) or a restriction of the (general-valued) valued constraint satisfaction problem (VCSP). Other optimisation versions of CSPs such as the minimum solution problem (Min-Sol) and the minimum ones problem (Min-Ones) are special cases of the extended Min-Cost-Hom.
The study of VCSPs has recently seen remarkable progress. A complete classification for the complexity of finite-valued languages on arbitrary finite domains has been obtained Thapper and Živný [STOC’13]. However, understanding the complexity of languages that are not finitevalued appears to be more difficult. The extended Min-Cost-Hom allows us to study problematic languages of this type without having to deal with with the full generality of the VCSP. A recent classification for the complexity of three-element Min-Sol, Uppman [ICALP’13], takes a step in this direction. In this paper we generalise this result considerably by determining the complexity of three-element extended Min-Cost-Hom.
Place, publisher, year, edition, pages
Dagstuhl: Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik , 2014. 651-662 p.
, Leibniz International Proceedings in Informatics, ISSN 1868-8969 ; 25
IdentifiersURN: urn:nbn:se:liu:diva-112916DOI: 10.4230/LIPIcs.STACS.2014.651ISBN: 978-3-939897-65-1OAI: oai:DiVA.org:liu-112916DiVA: diva2:773698
31st International Symposium on Theoretical Aspects of Computer Science (STACS-2014)