Soft Constraints: Complexity and Multimorphisms

Cohen, David A.; Cooper, Martin; Jeavons, Peter; Krokhin, Andrei

doi:10.1007/978-3-540-45193-8_17

Cited by 12 publications

(2 citation statements)

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“…It would interesting to explore methods of proving tractability of Max CSP other than via a reduction to submodular set function minimization (as in [8]) or via an explicit description of predicates (as in this paper). Can the technique of multimorphisms [6,7] be effectively used in the study of non-Boolean Max CSP? Another interesting direction for future work is to study approximability of hard Max CSP problems.…”

Section: Resultsmentioning

confidence: 99%

Maximum Constraint Satisfaction on Diamonds

Krokhin

Larose

2005

Principles and Practice of Constraint Programming - CP 2005

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Abstract. In this paper we study the complexity of the (weighted) maximum constraint satisfaction problem (Max CSP) over an arbitrary finite domain. In this problem, one is given a collection of weighted constraints on overlapping sets of variables, and the goal is to find an assignment of values to the variables so as to maximize the total weight of satisfied constraints. Max Cut is a typical example of a Max CSP problem. Max CSP is NP-hard in general; however, some restrictions on the form of constraints may ensure tractability. Recent results indicate that there is a connection between tractability of such restricted problems and supermodularity of the allowed constraint types with respect to some lattice ordering of the domain. We prove several results confirming this. Diamonds are the smallest lattices in terms of the number of comparabilities, and so are as unordered as a lattice can possibly be. In the present paper, we study Max CSP on diamond-ordered domains. We show that if all allowed constraints are supermodular with respect to such an ordering then the problem can be solved in polynomial (in fact, in cubic) time. We also prove a partial converse: if the set of allowed constraints includes a certain small family of binary supermodular constraints on such a lattice, then the problem is tractable if and only if all of the allowed constraints are supermodular; otherwise, it is NP-hard.

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Section: Resultsmentioning

confidence: 99%

Maximum Constraint Satisfaction on Diamonds

Krokhin

Larose

2005

Principles and Practice of Constraint Programming - CP 2005

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“…[2]). The two main approaches to soft constraint satisfaction problems, scsp [4] and vcsp [24,9], generalise the classical crisp variant of constraint satisfaction problems (csp) by evaluating constraints over c-semirings and valuation structures, respectively.…”

Section: Work Partially Supported By Funds From the Spanish Ministry mentioning

confidence: 99%

Many-Valued Institutions for Constraint Specification

Chiriźăź

Fiadeiro

Orejas

2016

Fundamental Approaches to Software Engineering

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Abstract. We advance a general technique for enriching logical systems with soft constraints, making them suitable for specifying complex software systems where parts are put together not just based on how they meet certain functional requirements but also on how they optimise certain constraints. This added expressive power is required, for example, for capturing quality attributes that need to be optimised or, more generally, for formalising what are usually called service-level agreements. More specifically, we show how institutions endowed with a graded semantic consequence can accommodate soft-constraint satisfaction problems. We illustrate our approach by showing how, in the context of service discovery, one can quantify the compatibility of two specifications and thus formalise the selection of the most promising provider of a required resource.

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