Supermodularity on chains and complexity of maximum constraint satisfaction

Abstract : In the maximum constraint satisfaction problem ($\mathrm{Max \; CSP}$), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maximise the number (or the total weight) of satisfied constraints. This problem is $\mathrm{NP}$-hard in general so it is natural to study how restricting the allowed types of constraints affects the complexity of the problem. In this paper, we show that any $\mathrm{Max \; CSP}$ problem with a finite set of allowed constraint types, which includes all constants (i.e. constraints of the form $x=a$), is either solvable in polynomial time or is $\mathrm{NP}$-complete. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description uses the well-known combinatorial property of supermodularity.
Type de document :
Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.51-56, 2005, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [11 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01184377
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 14 août 2015 - 11:38:25
Dernière modification le : jeudi 11 mai 2017 - 01:02:53
Document(s) archivé(s) le : dimanche 15 novembre 2015 - 11:03:41

Fichier

dmAE0111.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01184377, version 1

Collections

Citation

Vladimir Deineko, Peter Jonsson, Mikael Klasson, Andrei Krokhin. Supermodularity on chains and complexity of maximum constraint satisfaction. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.51-56, 2005, DMTCS Proceedings. 〈hal-01184377〉

Partager

Métriques

Consultations de la notice

250

Téléchargements de fichiers

53