Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
SIAM Journal on Discrete Mathematics
To cut…or not to cut (applications of comparative physical maps in molecular evolution)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
(1 + ɛ)-Approximation of sorting by reversals and transpositions
Theoretical Computer Science
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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Reversal, transposition and transreversal are common events in genome rearrangement. The genome rearrangement sorting problem is to transform one genome into another using the minimum number of rearrangement operations. Hannenhalli and Pevzner discovered that singleton is the major obstacle for unsigned reversal sorting. They also gave a polynomial algorithm for reversal sorting on those unsigned permutations with O(log n) singletons. This paper involves two aspects. (1)We describe one case for which Hannenhalli and Pevzner's algorithm may fail, and propose a corrected algorithm for unsigned reversal sorting. (2) We propose a (1+Ɛ)-approximation algorithmfor the weighted sorting problem on unsigned permutations with O(log n) singletons. Theweighted sortingmeans: sorting a permutation by weighted reversals, transpositions and transreversals, where reversal is assigned weight 1 and transposition(including transreversal) is assigned weight 2.