A Representation Theorem for Union-Difference Families and Application

Binh-Minh Bui-Xuan (1) , Michel Habib (2)

1 ALGCO - Algorithmes, Graphes et Combinatoire
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We give a quadratic O(|X|^2) space representation based on a canonical tree for any subset family F\subseteq 2^X closed under the union and the difference of its overlapping members. The cardinality of F is potentially in O(2^|^X|), and the total cardinality of its members even higher. As far as we know this is the first representation result for such families. As an application of this framework we obtain a unique digraph decomposition that not only captures, but also is strictly more powerful than the well-studied modular decomposition. A polynomial time decomposition algorithm for this case is described.

Domains: Discrete Mathematics [cs.DM]

Binh-Minh Bui-Xuan, Michel Habib. A Representation Theorem for Union-Difference Families and Application. LATIN: Latin American Symposium, Apr 2008, Búzios, Brazil. pp.492-503, ⟨10.1007/978-3-540-78773-0_43⟩. ⟨lirmm-00324969⟩