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Communication Dans Un Congrès Année : 2009

Unifying the representation of symmetric crossing families and weakly partitive families

Résumé

The family of non-trivial minimizers of a symmetric submodular function is symmetric crossing, namely it is closed under the complementation of any member and under the intersection of its crossing members. The family of modules of a graph is weakly partitive, namely it is closed under the intersection, union, and difference of its overlapping members. It is known that any symmetric crossing (resp. weakly partitive) family $F \subseteq 2^X$ has an $O(|X|)$ space representation. In a previous work we gave a general framework for representing any set family by a tree. This is a natural extension of the above mentioned result on symmetric crossing families. We here show how our framework also captures, in a non-trivial way, the above mentioned result on weakly partitive families. Among the consequences, this is the first result generalizing both the modular decomposition of a graph and the structural behaviour of the minimizers of a symmetric submodular function.

Dates et versions

hal-00555314 , version 1 (13-01-2011)

Identifiants

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Binh-Minh Bui-Xuan, Michel Habib. Unifying the representation of symmetric crossing families and weakly partitive families. European Conference on Combinatorics, Graph Theory and Applications (Eurocomb'09), 2009, Bordeaux, France. pp.329-333, ⟨10.1016/j.endm.2009.07.054⟩. ⟨hal-00555314⟩
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