A representation theorem for union-difference families and application

Authors:
B.-M. Bui-Xuan;M. Habib
Affiliations:
CNRS, LIRMM, Université Montpellier II, Montpellier Cedex 05, France;CNRS, LIAFA, Université Paris Diderot Paris 7, Paris Cedex 13, France
Venue:
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Year:
2008

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Abstract

We give a quadratic O(|X|2) space representation based on a canonical tree for any subset family F ⊆ 2X 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.