A note on a Maximum k-Subset Intersection problem

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"""[email protected][email protected]?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.