Constraint and Satisfiability Reasoning for Graph Coloring - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Article Dans Une Revue Journal of Artificial Intelligence Research Année : 2020

Constraint and Satisfiability Reasoning for Graph Coloring

Résumé

Graph coloring is an important problem in combinatorial optimization and a major component of numerous allocation and scheduling problems. In this paper we introduce a hybrid CP/SAT approach to graph coloring based on the addition-contraction recurrence of Zykov. Decisions correspond to either adding an edge between two non-adjacent vertices or contracting these two vertices, hence enforcing inequality or equality, respectively. This scheme yields a symmetry-free tree and makes learnt clauses stronger by not committing to a particular color. We introduce a new lower bound for this problem based on Mycielskian graphs; a method to produce a clausal explanation of this bound for use in a CDCL algorithm; a branching heuristic emulating Brélaz' heuristic on the Zykov tree; and dedicated pruning techniques relying on marginal costs with respect to the bound and on reasoning about transitivity when unit propagating learnt clauses. The combination of these techniques in both a branch-and-bound and in a bottom-up search outperforms other SAT-based approaches and Dsatur on standard benchmarks both for finding upper bounds and for proving lower bounds.
Fichier principal
Vignette du fichier
paper.pdf (538.63 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-02907062 , version 1 (31-08-2021)

Identifiants

Citer

Emmanuel Hébrard, George Katsirelos. Constraint and Satisfiability Reasoning for Graph Coloring. Journal of Artificial Intelligence Research, 2020, 69, ⟨10.1613/jair.1.11313⟩. ⟨hal-02907062⟩
128 Consultations
229 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More