A note on a Maximum k-Subset Intersection problem

Authors:
Eduardo C. Xavier
Affiliations:
Institute of Computing, University of Campinas - UNICAMP, Campinas, SP, Brazil
Venue:
Information Processing Letters
Year:
2012

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Abstract

Consider the following problem which we call Maximum k-Subset Intersection (MSI): Given a collection C={S"1,...,S"m} of m subsets over a finite set of elements E={e"1,...,e"n}, and a positive integer k, the objective is to select exactly k subsets S"j"""1,...,S"j"""k whose intersection size |S"j"""1@?...@?S"j"""k| is maximum. In [2], Clifford and Popa (2011) studied a related problem and left as an open problem the status of the MSI problem. In this paper we show that this problem is hard to approximate.