Encodings of the Sequence Constraint

Abstract. The SEQUENCE constraint is useful in modelling car sequencing, rostering, scheduling and related problems. We introduce half a dozen new encodings of the SEQUENCE constraint, some of which do not hinder propagation. We prove that down the whole branch of a search tree domain consistency can be enforced on the SEQUENCE constraint in just O(n2 log n) time. This improves upon the previous bound of O(n3 ) for each call down the tree. We also consider some generalizations including multiple SEQUENCE constraints, and cyclic SEQUENCE constraints. Our experiments suggest that, on very large and tight problems, domain consistency algorithms are best. However, on smaller or looser problems, much simpler encodings are better, even though these encodings hinder propagation. When there are multiple SEQUENCE constraints, a more expensive propagator shows promise.

• Type: Conference
• Year: 2007
• Where: CP
• Authors: Sebastian Brand, Nina Narodytska, Claude-Guy Quimper, Peter J. Stuckey, Toby Walsh
• Keywords: CP 2007, Domain Consistency, Multiple Sequence Constraints, Programming Languages, Sequence Constraints