Abstract

A collection of sets is called splittable if there is a set S such that for each set B in the collection, the intersection of S and B is half the size of B. Splittability is a generalization of graph colorability, which is an active area of research with numerous applications such as scheduling and matching. We show that the problem of deciding whether a collection is splittable is NP-complete. Nevertheless we characterize splittability for some special collections. Finally we study a further generalization called p-splittability, in which the splitter S is required to contain a given fraction of each set B.

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Poster #W10

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The Set Splittablity Problem

A collection of sets is called splittable if there is a set S such that for each set B in the collection, the intersection of S and B is half the size of B. Splittability is a generalization of graph colorability, which is an active area of research with numerous applications such as scheduling and matching. We show that the problem of deciding whether a collection is splittable is NP-complete. Nevertheless we characterize splittability for some special collections. Finally we study a further generalization called p-splittability, in which the splitter S is required to contain a given fraction of each set B.