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International Conference on Principles and Practice of Constraint Programming

CP 2010: Principles and Practice of Constraint Programming – CP 2010 pp 152–166Cite as

A New Hybrid Tractable Class of Soft Constraint Problems

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6308))

Abstract

The constraint satisfaction problem (CSP) is a central generic problem in artificial intelligence. Considerable effort has been made in identifying properties which ensure tractability in such problems. In this paper we study hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but properties which do not depend only on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity).

We firstly present two hybrid classes of soft constraint problems defined by forbidden subgraphs in the structure of the instance. These classes allow certain combinations of binary crisp constraints together with arbitrary unary soft constraints.

We then introduce the joint-winner property, which allows us to define a novel hybrid tractable class of soft constraint problems with soft binary and unary constraints. This class generalises the SoftAllDiff constraint with arbitrary unary soft constraints. We show that the joint-winner property is easily recognisable in polynomial time and present a polynomial-time algorithm based on maximum-flows for the class of soft constraint problems satisfying the joint-winner property. Moreover, we show that if cost functions can only take on two distinct values then this class is maximal.

Stanislav Živný gratefully acknowledges the support of EPSRC grant EP/F01161X/1, EPSRC PhD+ Award, and Junior Research Fellowship at University College, Oxford.

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Author information

Authors and Affiliations

  1. IRIT, University of Toulouse III, 31062, Toulouse, France

    Martin C. Cooper

  2. Computing Laboratory, University of Oxford, OX1 3QD, Oxford, UK

    Stanislav Živný

Authors
  1. Martin C. Cooper
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  2. Stanislav Živný
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, Surrey, United Kingdom

    David Cohen

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Cooper, M.C., Živný, S. (2010). A New Hybrid Tractable Class of Soft Constraint Problems. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-15396-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15395-2

  • Online ISBN: 978-3-642-15396-9

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