Filtering algorithms for the multiset ordering constraint

Authors:
Alan M. Frisch;Brahim Hnich;Zeynep Kiziltan;Ian Miguel;Toby Walsh
Affiliations:
Department of Computer Science, University of York, UK;Faculty of Computer Science, Izmir University of Economics, Turkey;Department of Computer Science, University of Bologna, Italy;School of Computer Science, University of St Andrews, UK;NICTA and School of Computer Science and Engineering, University of New South Wales, Australia
Venue:
Artificial Intelligence
Year:
2009

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Abstract

Constraint programming (CP) has been used with great success to tackle a wide variety of constraint satisfaction problems which are computationally intractable in general. Global constraints are one of the important factors behind the success of CP. In this paper, we study a new global constraint, the multiset ordering constraint, which is shown to be useful in symmetry breaking and searching for leximin optimal solutions in CP. We propose efficient and effective filtering algorithms for propagating this global constraint. We show that the algorithms maintain generalised arc-consistency and we discuss possible extensions. We also consider alternative propagation methods based on existing constraints in CP toolkits. Our experimental results on a number of benchmark problems demonstrate that propagating the multiset ordering constraint via a dedicated algorithm can be very beneficial.