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Journal of Combinatorial Optimization

, Volume 25, Issue 3, pp 339–351 | Cite as

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

  • Xin Chen
Article

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.

Keywords

Genome rearrangement Double-cut-and-joins Breakpoint graph decomposition Fractional linear programming 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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