On the Monotonicity of Process Number

Nicolas Nisse 1, 2 Ronan Soares 1, 3
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Graph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with treeand path-decomposition of graphs. In order to define decompositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider such a game that has been defined and studied in the context of routing reconfiguration problems in WDM networks. Namely, in the processing game, the fugitive is invisible, arbitrary fast, it moves in the opposite direction of the arcs of a digraph, but only as long as it has access to a strongly connected component free of searchers. We prove that the processing game is monotone which leads to its equivalence with a new digraph decomposition.
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Nicolas Nisse, Ronan Soares. On the Monotonicity of Process Number. 7th Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS), Apr 2013, Mexico, Mexico. pp.141-147. ⟨hal-00845539⟩

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