On the inapproximability of maximum intersection problems

Abstract

Given a sets, we want to choose exactly k sets such that the cardinality of their intersection is maximized. This is the so-called MAX-k-INTERSECT problem. We prove that MAX-k-INTERSECT cannot be approximated within an absolute error of 1/2n(1-2 epsilon) + O(n(1-3 epsilon)) unless P = NP. This answers an open question about its hardness. We also give a correct proof of an inapproximable result by Clifford and Papa (2011) [3] by proving that MAX-INTERSECT problem is equivalent to the MAX-CLIQUE problem. (C) 2012 Elsevier B.V. All rights reserved.