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Maximum Constraint Satisfaction on Diamonds

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 3709)

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 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 in a special case when the lattice ordering is as loose as possible, i.e., a diamond one.

Keywords

  • Constraint Satisfaction
  • Constraint Satisfaction Problem
  • Optimal Assignment
  • Submodular Function
  • Unary Predicate

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Krokhin, A., Larose, B. (2005). Maximum Constraint Satisfaction on Diamonds. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_30

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  • DOI: https://doi.org/10.1007/11564751_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29238-8

  • Online ISBN: 978-3-540-32050-0

  • eBook Packages: Computer ScienceComputer Science (R0)