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International Computing and Combinatorics Conference

COCOON 2010: Computing and Combinatorics pp 439–448Cite as

On Sorting Permutations by Double-Cut-and-Joins

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

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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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

    Xin Chen

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  1. Xin Chen
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Editors and Affiliations

  1. University of Florida, CSE Building, Room 566, P.O. Box 116120, 32611-6120, Gainesville, Florida, USA

    My T. Thai

  2. Department of Computer and Information Science and Technology, University of Florida, P.O. Box, USA

    Sartaj Sahni

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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

  • eBook Packages: Computer ScienceComputer Science (R0)

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