Maximum subset intersection

  • Authors:
  • Raphaël Clifford;Alexandru Popa

  • Affiliations:
  • University of Bristol, Department of Computer Science, Merchant Venturer's Building, Woodland Road Bristol, BS8 1UB, United Kingdom;University of Bristol, Department of Computer Science, Merchant Venturer's Building, Woodland Road Bristol, BS8 1UB, United Kingdom

  • Venue:
  • Information Processing Letters
  • Year:
  • 2011

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Abstract

Consider the following problem. Given u sets of sets A"1,...,A"u with elements over a universe E={e"1,...,e"n}, the goal is to select exactly one set from each of A"1,...,A"u in order to maximize the size of the intersection of the sets. In this paper we present a gap-preserving reduction from Max-Clique which enables us to show that our problem cannot be approximated within an n^1^-^@e multiplicative factor, for any @e0, unless P=NP (Zuckerman, 2006 [12]).