A Novel Greedy Algorithm for the Minimum Common String Partition Problem

Abstract

The Minimum Common String Partition problem (MCSP) is to partition two given input strings into the same collection of substrings, where the number of substrings in the partition is minimized. This problem is a key problem in genome rearrangement, and is closely related to the problem of sorting by reversals with duplicates. MCSP is NP-hard, even for the most trivial case, 2-MCSP, where each letter occurs at most twice in each input string. There are various approximation algorithms which can achieve very good approximation ratios but with complicated implementations, for example, 1.5-approximation algorithm for 2-MCSP, 1.1037-approximation algorithm for 2-MCSP and a 4-approximation algorithm for 3-MCSP. There is also a simple greedy algorithm for MCSP which extracts the longest common substring from the given strings at each step. In this paper, we propose a novel greedy algorithm for MCSP, where we extract the longest common substring containing a symbol occurring only once at each step whenever there is a such symbol. We show our algorithm is more “worst case” greedy at each step than the greedy algorithm and the expected performance of our algorithm is better than that of the greedy algorithm. Our experiments show that our method achieves a better partition on average than the greedy algorithm does. Another advantage of our algorithm is that it is much faster than the greedy algorithm.