Vladimir Deineko ; Peter Jonsson ; Mikael Klasson ; Andrei Krokhin
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Supermodularity on chains and complexity of maximum constraint satisfaction
dmtcs:3420 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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https://doi.org/10.46298/dmtcs.3420
Supermodularity on chains and complexity of maximum constraint satisfactionConference paper
Authors: Vladimir Deineko 1; Peter Jonsson 2; Mikael Klasson 2; Andrei Krokhin 3
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Vladimir Deineko;Peter Jonsson;Mikael Klasson;Andrei Krokhin
1 Warwick Business School
2 Department of Computer and Information Science - Linköping University
3 School of Engineering and Computing Sciences
In the maximum constraint satisfaction problem (MaxCSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maximise the number (or the total weight) of satisfied constraints. This problem is NP-hard in general so it is natural to study how restricting the allowed types of constraints affects the complexity of the problem. In this paper, we show that any MaxCSP problem with a finite set of allowed constraint types, which includes all constants (i.e. constraints of the form x=a), is either solvable in polynomial time or is NP-complete. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description uses the well-known combinatorial property of supermodularity.
Peter Jonsson;Andrei Krokhin;Fredrik Kuivinen, Lecture notes in computer science, Ruling Out Polynomial-Time Approximation Schemes for Hard Constraint Satisfaction Problems, pp. 182-193, 2007, 10.1007/978-3-540-74510-5_20.