Minimum common string partition revisited

Authors:
Haitao Jiang;Binhai Zhu;Daming Zhu;Hong Zhu
Affiliations:
Department of Computer Science, Montana State University, Bozeman, MT and School of Computer Science and Technology, Shandong University, Jinan, China;Department of Computer Science, Montana State University, Bozeman, MT;School of Computer Science and Technology, Shandong University, Jinan, China;College of Software, East China Normal University, Shanghai, China
Venue:
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Year:
2010

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Abstract

Minimum Common String Partition (MCSP) has drawn much attention due to its application in genome rearrangement. In this paper, we investigate three variants of MCSP: MCSPc, which requires that there are at most c symbols in the alphabet; d-MCSP, which requires the occurrence of each symbol to be bounded by d; and x-balance MCSP, which requires the length of blocks not being x away from the average length. We show that MCSPc is NP-hard when c ≥ 2. As for d-MCSP, we present an FPT algorithm which runs in O*((d!)k) time. As it is still unknown whether an FPT algorithm only parameterized on k exists for the general case of MCSP, we also devise an FPT algorithm for the special case x-balance MCSP parameterized on both k and x.