Efficient Implementation of the Global Cardinality Constraint with Costs

TL;DR

This paper introduces a fast, landmark-based preprocessing approach for efficiently implementing the global cardinality constraint with costs in constraint programming, improving practical filtering performance.

Contribution

It proposes a novel landmark-based method to efficiently handle shortest path computations in the cardinality constraint with costs, enhancing practical filtering algorithms.

Findings

Reduces computational effort in filtering algorithms

Preprocessing with landmarks speeds up shortest path calculations

Improves practical efficiency of global cardinality constraints with costs

Abstract

The success of Constraint Programming relies partly on the global constraints and implementation of the associated filtering algorithms. Recently, new ideas emerged to improve these implementations in practice, especially regarding the all different constraint. In this paper, we consider the cardinality constraint with costs. The cardinality constraint is a generalization of the all different constraint that specifies the number of times each value must be taken by a given set of variables in a solution. The version with costs introduces an assignment cost and bounds the total sum of assignment costs. The arc consistency filtering algorithm of this constraint is difficult to use in practice, as it systematically searches for many shortest paths. We propose a new approach that works with upper bounds on shortest paths based on landmarks. This approach can be seen as a preprocessing. It is fast and avoids, in practice, a large number of explicit computations of shortest paths.