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On Sorting Permutations by Double-Cut-and-Joins

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Computing and Combinatorics (COCOON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

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Abstract

The problem of sorting 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.

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Chen, X. (2010). On Sorting Permutations by Double-Cut-and-Joins. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_47

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  • DOI: https://doi.org/10.1007/978-3-642-14031-0_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

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