Abstract
Given two strings S and S′ of the same length, the Minimum Common String Partition (MCSP) is to partition them into the minimum number of strings S = S 1·S 2 ⋯ S k and S′ = S 1′·S 2′ ⋯ S k ′ such that the substrings 〈S 1′,S 2′, ⋯ , S k ′〉 is a permutation of 〈S 1,S 2, ⋯ ,S k 〉. MCSP is an NP-complete problem originating from computational genomics. There exists constant-factor approximations for some special cases, but the factors are impractical. On exact solutions, it is open whether there exists an FPT algorithm for the general case and some inefficient FPT algorithms for very special cases. In this paper, we present an O(2n n O(1)) time algorithm for the general case. We also show an O(n (logn)2) time algorithm which solves the case for almost all strings S and S′ if the length of each block in their minimum common partition is at least \({d_0\log n\over \log t}\) for some positive constant d 0, where t is the size of the alphabet Σ.
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Fu, B., Jiang, H., Yang, B., Zhu, B. (2011). Exponential and Polynomial Time Algorithms for the Minimum Common String Partition Problem. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_24
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DOI: https://doi.org/10.1007/978-3-642-22616-8_24
Publisher Name: Springer, Berlin, Heidelberg
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