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Propagating conjunctions of AllDifferent constraints

Authors

Christian Bessiere, Georgios Katsirelos, Nina Narodytska, Claude-Guy Quimper and Toby Walsh

LIRMM

CNRS

NICTA

UNSW

Abstract

We study propagation algorithms for the conjunction of two ALLDIFFERENT constraints. Solutions of an ALLDIFFERENT constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of finding simultaneous bipartite matchings. We present an extension of the famous Hall theorem which characterizes when simultaneous bipartite matchings exists. Unfortunately, finding such matchings is NP-hard in general. However, we prove a surprising result that finding a simultaneous matching on a convex bipartite graph takes just polynomial time. Based on this theoretical result, we provide the first polynomial time bound consistency algorithm for the conjunction of two ALLDIFFERENT constraints. We identify a pathological problem on which this propagator is exponentially faster compared to existing propagators. Our experiments show that this new propagator can offer significant benefits over existing methods.

BibTeX Entry

  @inproceedings{Bessiere_KNQW_10,
    publisher        = {AAAI Press},
    author           = {Bessiere, Christian and Katsirelos, Georgios and Narodytska, Nina and Quimper, Claude-Guy and Walsh,
                        Toby},
    month            = jul,
    year             = {2010},
    title            = {Propagating Conjunctions of {AllDifferent} Constraints},
    booktitle        = {Twenty-Fourth AAAI Conference on Artificial Intelligence (AAAI-10)},
    pages            = {27--32},
    address          = {Atlanta, USA}
  }

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