Abstract
In the Minimum Common String Partition problem (MCSP) we are given two strings on input, and we wish to partition them into the same collection of substrings, minimimizing the number of the substrings in the partition. Even a special case, denoted 2-MCSP, where each letter occurs at most twice in each input string, is NP-hard. We study a greedy algorithm for MCSP that at each step extracts a longest common substring from the given strings. We show that the approximation ratio of this algorithm is between Ω(n 0.43) and O(n 0.69). In case of 2-MCSP, we show that the approximation ratio is equal to 3. For 4-MCSP, we give a lower bound of Ω(log n).
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© 2004 Springer-Verlag Berlin Heidelberg
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Chrobak, M., Kolman, P., Sgall, J. (2004). The Greedy Algorithm for the Minimum Common String Partition Problem. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2004 2004. Lecture Notes in Computer Science, vol 3122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27821-4_8
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DOI: https://doi.org/10.1007/978-3-540-27821-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22894-3
Online ISBN: 978-3-540-27821-4
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