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Computational Complexity of the Minimum Cost Homomorphism Problem on Three-element DomainsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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Number of Authors: 12014 (English)Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Dagstuhl: Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik , 2014. p. 651-662
##### Series

Leibniz International Proceedings in Informatics, ISSN 1868-8969 ; 25
##### National Category

Computer Sciences
##### Identifiers

URN: urn:nbn:se:liu:diva-112916DOI: 10.4230/LIPIcs.STACS.2014.651ISBN: 978-3-939897-65-1 (print)OAI: oai:DiVA.org:liu-112916DiVA, id: diva2:773698
##### Conference

31st International Symposium on Theoretical Aspects of Computer Science (STACS-2014)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2014-12-19 Created: 2014-12-19 Last updated: 2018-01-11
##### In thesis

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.

1. On Some Combinatorial Optimization Problems: Algorithms and Complexity$(function(){PrimeFaces.cw("OverlayPanel","overlay806491",{id:"formSmash:j_idt720:0:j_idt724",widgetVar:"overlay806491",target:"formSmash:j_idt720:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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