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).


Greedy Algorithm Approximation Ratio Edit Distance Optimal Partition Common Substring 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Marek Chrobak
    • 1
  • Petr Kolman
    • 1
    • 2
  • Jiří Sgall
    • 3
  1. 1.Department of Computer ScienceUniversity of CaliforniaRiversideUSA
  2. 2.Institute for Theoretical Computer ScienceCharles UniversityPraha 1Czech Republic
  3. 3.Mathematical InstitutePraha 1Czech Republic

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