On the Exact Block Cover Problem

Minimum Common String Partition (MCSP) has drawn a lot of attention due to its application in genome rearrangement. The best approximation algorithm has a factor O(lognlog* n) and it was shown most recently that it is FPT (but with a very high running time). In this paper, we consider the decision version of the one-sided MCSP problem (formally called the exact block cover problem); namely, when one sequence is already partitioned into k blocks, how to decide whether the other sequence can be partitioned accordingly. While this decision problem is obviously in FPT, we show interesting results in this paper: (1) If each letter is allowed to appear at most twice (or three times), then the problem is polynomially solvable, (2) There is an FPT algorithm which runs in O *(2 k ) time, improving the trivial bound of O *(k!), and (3) If |Σ| = c, c being a constant at least 2, then the problem is NP-complete.

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