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 elements in the alphabet; d-MCSP, which requires the occurrence of each element to be bounded by d; and x-balanced MCSP, which requires the length of blocks being in range (n/k−x,n/k+x), where n is the length of the input strings, k is the number of blocks in the optimal common partition and x is a constant integer. We show that MCSPc is NP-hard when c≥2. As for d-MCSP, we present an FPT algorithm which runs in O ∗((d!)2k) 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-balanced MCSP parameterized on both k and x.
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Jiang, H., Zhu, B., Zhu, D. et al. Minimum common string partition revisited. J Comb Optim 23, 519–527 (2012). https://doi.org/10.1007/s10878-010-9370-2
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DOI: https://doi.org/10.1007/s10878-010-9370-2