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A 14/11-approximation algorithm for sorting by short block-moves

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Abstract

Block-move is one of the popular operations for genome rearrangement. A short block-move is an operation on a permutation that moves an element at most two positions away from its original position. Heath and Vergara investigated the problem of finding a minimum-length sorting sequence of short block-moves for a given permutation and devised a 4/3-approximation algorithm. In this paper, we present a new 14/11-approximation algorithm for this problem. Firstly, we devise an exact polynomial time algorithm for sorting a special kind of sub-permutations called umbrella; then we split the permutation into a series of related umbrellas and sort them greedily. We obtain a new lower bound of the short block-move distance by exploiting the properties of five kinds of sub-permutations. After some complicated analysis, we prove that the approximation ratio of the new algorithm is at most 14/11.

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Jinan, 250101, China

    HaiTao Jiang & DaMing Zhu

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  1. HaiTao Jiang
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  2. DaMing Zhu
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Correspondence to DaMing Zhu.

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Jiang, H., Zhu, D. A 14/11-approximation algorithm for sorting by short block-moves. Sci. China Inf. Sci. 54, 279–292 (2011). https://doi.org/10.1007/s11432-010-4131-5

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  • DOI: https://doi.org/10.1007/s11432-010-4131-5

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