Reformulating global constraints: the slide and regular constraints

Authors:
Christian Bessiere;Emmanuel Hebrard;Brahim Hnich;Zeynep Kiziltan;Claude-Guy Quimper;Toby Walsh
Affiliations:
LIRMM, University of Montpellier, France;University College Cork, Ireland;Faculty of Computer Science, Izmir University of Economics, Turkey;Department of Computer Science, University of Bologna, Italy;Omega Optimisation, Canada;NICTA and University of New South Wales, Sydney, Australia
Venue:
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
Year:
2007

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Abstract

Global constraints are useful for modelling and reasoning about real-world combinatorial problems. Unfortunately, developing propagation algorithms to reason about global constraints efficiently and effectively is usually a difficult and complex process. In this paper, we show that reformulation may be helpful in building such propagators. We consider both hard and soft forms of two powerful global constraints, Slide and Regular. These global constraints are useful to represent a wide range of problems like rostering and scheduling where we have a sequence of decision variables and some constraint that holds along the sequence. We show that the different forms of Slide and Regular can all be reformulated as each other. We also show that reformulation is an effective method to incorporate such global constraints within an existing constraint toolkit. Finally, this study provides insight into the close relationship between these two important global constraints.