Flow-Based Propagators for the SEQUENCE and Related Global Constraints

TL;DR

This paper introduces flow-based algorithms for the SEQUENCE constraint that achieve domain consistency efficiently, improving computational complexity and offering new ways to handle large domains in global constraints.

Contribution

It presents novel flow-based filtering algorithms for the SEQUENCE constraint, enhancing efficiency and extending applicability to related constraints.

Findings

Achieves domain consistency in O(n^2) time, faster than previous methods.

Uses linear programming-derived flows for efficient propagation.

Potentially applicable to other global constraints with large domains.

Abstract

We propose new filtering algorithms for the SEQUENCE constraint and some extensions of the SEQUENCE constraint based on network flows. We enforce domain consistency on the SEQUENCE constraint in $O(n^2)$ time down a branch of the search tree. This improves upon the best existing domain consistency algorithm by a factor of $O(\log n)$. The flows used in these algorithms are derived from a linear program. Some of them differ from the flows used to propagate global constraints like GCC since the domains of the variables are encoded as costs on the edges rather than capacities. Such flows are efficient for maintaining bounds consistency over large domains and may be useful for other global constraints.