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.
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Chen, X. On sorting unsigned permutations by double-cut-and-joins. J Comb Optim 25, 339–351 (2013). https://doi.org/10.1007/s10878-010-9369-8
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DOI: https://doi.org/10.1007/s10878-010-9369-8