A Representation Theorem for union-difference Families and Application

Binh-Minh Bui-Xuan 1 Michel Habib 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We give a quadratic $O(|X|^2)$ space representation based on a canonical tree for any subset family $F\subseteq2^X$ holding the closure under union and difference of overlapping members. The cardinal of $F$ is potentially in $O(2^{|X|})$, and its size higher. As far as we know this is the first representation theorem for such families. As an application of this framework we obtain a uniqueness decomposition theorem on a digraph decomposition that captures and is strictly more powerful than the well-studied modular decomposition. Moreover a polynomial time decomposition algorithm for this case is described.
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[Research Report] RR-07020, LIRMM. 2007
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Contributeur : Binh-Minh Bui-Xuan <>
Soumis le : mercredi 30 janvier 2008 - 16:24:45
Dernière modification le : jeudi 11 janvier 2018 - 06:26:13
Document(s) archivé(s) le : mardi 21 septembre 2010 - 15:16:28

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Binh-Minh Bui-Xuan, Michel Habib. A Representation Theorem for union-difference Families and Application. [Research Report] RR-07020, LIRMM. 2007. 〈lirmm-00175766v2〉

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