Minimum Common String Partition Revisited

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: MCSP , 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 MCSP c is NP-hard when c ≥ 2. As for d-MCSP, we present an FPT algorithm which runs in O((d!)) 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.