The Greedy Algorithm for the Minimum Common String Partition Problem
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(n0.43) and O(n0.69). 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).
Unable to display preview. Download preview PDF.
- 1.Chen, X., Zheng, J., Fu, Z., Nan, P., Zhong, Y., Lonardi,S., Jiang, T.: Assignment of orthologous genes via genome rearrangement. (2004) (submitted) Google Scholar
- 2.Cormode, G., Muthukrishnan, J.A.: The string edit distance matching with moves. In: Proc. 13th Annual Symposium on Discrete Algorithms (SODA), pp. 667–676 (2002)Google Scholar
- 3.Goldstein, A., Kolman, P., Zheng, J.: Minimum common string partitioning problem: Hardness and approximations (2004) (manuscript) Google Scholar
- 4.Kruskal, J.B., Sankoff, D.: An anthology of algorithms and concepts for sequence comparison. In: Sankoff, D., Kruskal, J.B. (eds.) Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison-Wesley, Reading (1983)Google Scholar
- 7.Shapira, D., Storer, J.A.: Edit distance with move operations. In: Proc. 13th Annual Symposium on Combinatorial Pattern Matching (CPM), pp. 85–98 (2002)Google Scholar