A linear kernel for the complementary maximal strip recovery problem

Authors:
Haitao Jiang;Binhai Zhu
Affiliations:
School of Computer Science and Technology, Shandong University, Jinan, Shandong, China,School of Mathematics and System Science, Shandong University, Jinan, Shandong, China;Department of Computer Science, Montana State University, Bozeman, MT
Venue:
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Year:
2012

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Abstract

In this paper, we compute the first linear kernel for the complementary problem of Maximal Strip Recovery (CMSR) -- a well-known NP-complete problem in computational genomics. Let k be the parameter which represents the size of the solution. The core of the technique is to first obtain a tight 18k bound on the parameterized solution search space, which is done through a mixed global rules and local rules, and via an inverse amortized analysis. Then we apply additional data-reduction rules to obtain a tight 84k kernel for the problem. Combined with the known algorithm using bounded degree search, we obtain the best FPT algorithm for CMSR to this date, running in O(2.36kk2+n2) time.