Maximum subset intersection

Consider the following problem. Given n sets of sets A1, . . . , Au with elements over a universe E = {e1, . . . , en}, the goal is to select exactly one set from each of A1, . . . , Au in order to maximize the size of the intersection of the sets. In this paper we present two NP-Hardness proofs, the first via a direct reduction from 3-Sat. The second proof involves a gap-preserving reduction from MaxClique which enables us to show that our problem cannot be approximated within an n1− multiplicative factor, for any > 0, unless NP = ZPP.

• Type: Journal
• Year: 2011
• Where: IPL
• Authors: Raphaël Clifford, Alexandru Popa
• Keywords: Gap-preserving Reduction, IPL 2011, N1− Multiplicative Factor, NP-Hardness Proofs