Probabilistic graph-coloring in bipartite and split graphs

N. Bourgeois (), F. Della Croce (), B. Escoffier (), C. Murat () and V. Th. Paschos ()
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N. Bourgeois: CNRS UMR 7024 and Université Paris-Dauphine
F. Della Croce: Politecnico di Torino
B. Escoffier: CNRS UMR 7024 and Université Paris-Dauphine
C. Murat: CNRS UMR 7024 and Université Paris-Dauphine
V. Th. Paschos: CNRS UMR 7024 and Université Paris-Dauphine

Journal of Combinatorial Optimization, 2009, vol. 17, issue 3, No 3, 274-311

Abstract: Abstract We revisit in this paper the stochastic model for minimum graph-coloring introduced in (Murat and Paschos in Discrete Appl. Math. 154:564–586, 2006), and study the underlying combinatorial optimization problem (called probabilistic coloring) in bipartite and split graphs. We show that the obvious 2-coloring of any connected bipartite graph achieves standard-approximation ratio 2, that when vertex-probabilities are constant probabilistic coloring is polynomial and, finally, we propose a polynomial algorithm achieving standard-approximation ratio 8/7. We also handle the case of split graphs. We show that probabilistic coloring is NP-hard, even under identical vertex-probabilities, that it is approximable by a polynomial time standard-approximation schema but existence of a fully a polynomial time standard-approximation schema is impossible, even for identical vertex-probabilities, unless P=NP. We finally study differential-approximation of probabilistic coloring in both bipartite and split graphs.

Keywords: Probabilistic optimization; Approximation algorithms; Graph coloring (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10878-007-9112-2

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