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On sorting unsigned permutations by double-cut-and-joins

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  • Xin Chen

    (Nanyang Technological University)

Abstract

The problem of sorting unsigned permutations by double-cut-and-joins (SBD) arises when we perform the double-cut-and-join (DCJ) operations on pairs of unichromosomal genomes without the gene strandedness information. In this paper we show it is a NP-hard problem by reduction to an equivalent previously-known problem, called breakpoint graph decomposition (BGD), which calls for a largest collection of edge-disjoint alternating cycles in a breakpoint graph. To obtain a better approximation algorithm for the SBD problem, we made a suitable modification to Lin and Jiang’s algorithm which was initially proposed to approximate the BGD problem, and then carried out a rigorous performance analysis via fractional linear programming. The approximation ratio thus achieved for the SBD problem is $\frac{17}{12}+\epsilon \approx 1.4167 +\epsilon$ , for any positive ε.

Suggested Citation

  • Xin Chen, 2013. "On sorting unsigned permutations by double-cut-and-joins," Journal of Combinatorial Optimization, Springer, vol. 25(3), pages 339-351, April.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:3:d:10.1007_s10878-010-9369-8
    DOI: 10.1007/s10878-010-9369-8
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    References listed on IDEAS

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    1. Guohui Lin & Tao Jiang, 2004. "A Further Improved Approximation Algorithm for Breakpoint Graph Decomposition," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 183-194, June.
    2. Alberto Caprara & Romeo Rizzi, 2002. "Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 157-182, June.
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    Cited by:

    1. Alexsandro Oliveira Alexandrino & Guilherme Henrique Santos Miranda & Carla Negri Lintzmayer & Zanoni Dias, 2021. "Length-weighted $$\lambda $$ λ -rearrangement distance," Journal of Combinatorial Optimization, Springer, vol. 41(3), pages 579-602, April.

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