On the inapproximability of maximum intersection problems

Authors:
Min-Zheng Shieh;Shi-Chun Tsai;Ming-Chuan Yang
Affiliations:
Information and Communications Technology Labs, National Chiao Tung University, Hsinchu, Taiwan;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan
Venue:
Information Processing Letters
Year:
2012

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Abstract

Given u 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 12n^1^-^2^@e+O(n^1^-^3^@e) unless P=NP. This answers an open question about its hardness. We also give a correct proof of an inapproximable result by Clifford and Popa (2011) [3] by proving that MAX-INTERSECT problem is equivalent to the MAX-CLIQUE problem.