Probabilistic coloring of bipartite and split graphs
Della Croce, Federico; Escoffier, Bruno; Murat, Cécile; Paschos, Vangelis (2005), Probabilistic coloring of bipartite and split graphs, in Gervasi, Osvaldo; Gavrilova, Marina; Kumar, Vipin; Lagana, Antonio; Lee, Heow Pueh; Mun, Youngsong; Taniar, David; Tan, Chih Jeng Kenneth, Computational Science and Its Applications - ICCSA 2005 International Conference, Singapore, May 9-12, 2005, Proceedings, Part IV, Springer : Berlin, p. 91-97. http://dx.doi.org/10.1007/11424925_23
TypeCommunication / Conférence
Conference titleInternational Conference on Computational Science and Its Applications (ICCSA'05)
Book titleComputational Science and Its Applications - ICCSA 2005 International Conference, Singapore, May 9-12, 2005, Proceedings, Part IV
Book authorGervasi, Osvaldo; Gavrilova, Marina; Kumar, Vipin; Lagana, Antonio; Lee, Heow Pueh; Mun, Youngsong; Taniar, David; Tan, Chih Jeng Kenneth
Series titleLecture Notes in Computer Science
Number of pages1362
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Abstract (EN)We revisit in this paper the probabilistic coloring problem (probabilistic coloring) and focus ourselves on bipartite and split graphs. We first give some general properties dealing with the optimal solution. We then show that the unique 2-coloring achieves approximation ratio 2 in bipartite graphs under any system of vertex-probabilities and propose a polynomial algorithm achieving tight approximation ratio 8/7 under identical vertex-probabilities. Then we deal with restricted cases of bipartite graphs. Main results for these cases are the following. Under non-identical vertex-probabilities probabilistic coloring is polynomial for stars, for trees with bounded degree and a fixed number of distinct vertex-probabilities, and, consequently, also for paths with a fixed number of distinct vertex-probabilities. Under identical vertex-probabilities, probabilistic coloring is polynomial for paths, for even and odd cycles and for trees whose leaves are either at even or at odd levels. Next, we deal with split graphs and show that probabilistic coloring is NP-hard, even under identical vertex-probabilities. Finally, we study approximation in split graphs and provide a 2-approximation algorithm for the case of distinct probabilities and a polynomial time approximation schema under identical vertex-probabilities.
Subjects / KeywordsPolynomial algorithm; coloring problem; Approximation algorithms
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Murat, Cécile; Escoffier, Bruno; Della Croce, Federico; Bourgeois, Nicolas; Paschos, Vangelis (2009) Article accepté pour publication ou publié
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