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Extensions of the Minimum Cost Homomorphism ProblemPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)In: Proceedings of the 16th Annual International Computing and Combinatorics Conference, Berlin: Springer , 2010, 328-337 p.Conference paper (Refereed)
##### Abstract [en]

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

Berlin: Springer , 2010. 328-337 p.
##### Series

, Lecture Notes in Computer Science, ISSN 0302-9743 ; 6196
##### National Category

Computer Science
##### Identifiers

URN: urn:nbn:se:liu:diva-63678DOI: 10.1007/978-3-642-14031-0_36ISBN: 978-3-642-14030-3 (print)ISBN: 978-3-642-14031-0 (online)OAI: oai:DiVA.org:liu-63678DiVA: diva2:382145
##### Conference

16th Annual International Computing and Combinatorics Conference, COCOON 2010; Nha Trang; Viet Nam
#####

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Available from: 2010-12-29 Created: 2010-12-29 Last updated: 2014-09-30Bibliographically approved

Assume *D* is a finite set and *R* is a finite set of functions from *D* to the natural numbers. An instance of the minimum *R*-cost homomorphism problem (*MinHom* _{R }) is a set of variables *V* subject to specified constraints together with a positive weight *c* _{vr } for each combination of *v* ∈ *V* and *r* ∈ *R*. The aim is to find a function *f*:*V* →*D* such that *f* satisfies all constraints and ∑ _{ v ∈ V } ∑ _{ r ∈ R } *c* _{vr } *r*(*f*(*v*)) is maximized.

This problem unifies well-known optimization problems such as the minimum cost homomorphism problem and the maximum solution problem, and this makes it a computationally interesting fragment of the valued CSP framework for optimization problems. We parameterize *MinHom* _{R } by *constraint languages*, i.e. sets Γ of relations that are allowed in constraints. A constraint language is called *conservative* if every unary relation is a member of it; such constraint languages play an important role in understanding the structure of constraint problems. The dichotomy conjecture for *MinHom* _{R } is the following statement: if Γ is a constraint language, then *MinHom* _{R } is either polynomial-time solvable or NP-complete. For *MinHom* the dichotomy result has been recently obtained [Takhanov, STACS, 2010] and the goal of this paper is to expand this result to the case of *MinHom* _{R } with conservative constraint language. For arbitrary *R* this problem is still open, but assuming certain restrictions on *R* we prove a dichotomy. As a consequence of this result we obtain a dichotomy for the conservative maximum solution problem

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