On sorting permutations by double-cut-and-joins

Authors:
Xin Chen
Affiliations:
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Venue:
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Year:
2010

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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 17/12 + ε ≅ 1.4167 + ε, for any positive ε.