Genome Rearrangement Algorithms for Unsigned Permutations with O(logn) Singletons

Abstract

Abstract. 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· )-approximation algorithm for the weighted sorting problem on unsigned permutations with O(log n) singletons. The weighted sorting means: sorting a permutation by weighted reversals, transpositions and transreversals, where reversal is assigned weight 1 and transposition(including transreversal) is assigned weight 2.