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Efficient Implementation of the Global Cardinality Constraint with Costs

Authors Margaux Schmied , Jean-Charles Régin

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Author Details

Margaux Schmied
  • Université Côte d'Azur, CNRS, I3S, Sophia Antipolis, France
Jean-Charles Régin
  • Université Côte d'Azur, CNRS, I3S, Sophia Antipolis, France

Funding

This work has been supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002.

Cite As Get BibTex

Margaux Schmied and Jean-Charles Régin. Efficient Implementation of the Global Cardinality Constraint with Costs. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CP.2024.27

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Planning for deterministic actions
  • Theory of computation → Constraint and logic programming
Keywords
  • global constraint
  • filtering algorithm
  • cardinality constraints with costs
  • arc consistency

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