On the Exact Block Cover Problem.
ALGORITHMIC ASPECTS IN INFORMATION AND MANAGEMENT, AAIM 2014(2014)
摘要
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(log n log* 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 vertical bar Sigma vertical bar = c, c being a constant at least 2, then the problem is NP-complete.
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关键词
Bipartite Graph, Genome Rearrangement, Dynamic Programming Algorithm, Edit Distance, Input String
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