In this paper we present an improved branch and bound algorithm for the vertex coloring problem. The idea is to try to extend the coloring of a maximum clique to its adjacent vertices. If this succeeds, its successive neighbors are considered; in case of failure (i.e., in the case the initial colors are not sufficient), working on the subgraph induced by the maximum clique and its neighborhood, the lower bound is improved by seeking for an optimal coloring of this subgraph by branch and bound. The process is repeated iteratively until the whole graph is examined. The iterative scheme exploits a further lower bound obtained by integrating a simple algorithm into the maximum clique search, and a new method to compute upper bounds on subgraphs. Furthermore, a new branching rule and a method for the selection of the initial maximum clique are presented. Extensive computational results and comparisons with existing exact coloring algorithms on random graphs and benchmarks are given

Iterative Coloring Extension of a Maximum Clique / Caramia, M.; Dell'Olmo, Paolo. - In: NAVAL RESEARCH LOGISTICS. - ISSN 0894-069X. - STAMPA. - 48:(2001), pp. 1-33. [10.1002/nav.1033]

Iterative Coloring Extension of a Maximum Clique

DELL'OLMO, Paolo
2001

Abstract

In this paper we present an improved branch and bound algorithm for the vertex coloring problem. The idea is to try to extend the coloring of a maximum clique to its adjacent vertices. If this succeeds, its successive neighbors are considered; in case of failure (i.e., in the case the initial colors are not sufficient), working on the subgraph induced by the maximum clique and its neighborhood, the lower bound is improved by seeking for an optimal coloring of this subgraph by branch and bound. The process is repeated iteratively until the whole graph is examined. The iterative scheme exploits a further lower bound obtained by integrating a simple algorithm into the maximum clique search, and a new method to compute upper bounds on subgraphs. Furthermore, a new branching rule and a method for the selection of the initial maximum clique are presented. Extensive computational results and comparisons with existing exact coloring algorithms on random graphs and benchmarks are given
2001
GRAPH; ALGORITMI
01 Pubblicazione su rivista::01a Articolo in rivista
Iterative Coloring Extension of a Maximum Clique / Caramia, M.; Dell'Olmo, Paolo. - In: NAVAL RESEARCH LOGISTICS. - ISSN 0894-069X. - STAMPA. - 48:(2001), pp. 1-33. [10.1002/nav.1033]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/48639
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