Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
429000 | Information Processing Letters | 2012 | 5 Pages |
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 12n1−2ϵ+O(n1−3ϵ) unless P=NPP=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.
► We study the hardness of two maximum intersection problems. ► We prove that MAX-INTERSECT problem is equivalent to the MAX-CLIQUE problem. ► We prove that MAX-k -INTERSECT problem cannot be approximated within an absolute error factor unless P=NPP=NP.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Min-Zheng Shieh, Shi-Chun Tsai, Ming-Chuan Yang,