Approximating the double-cut-and-join distance between unsigned genomes

作者：Chen Xin^*; Sun Ruimin; Yu Jiadong

来源：BMC Bioinformatics, 2011, 12: S17.

DOI：10.1186/1471-2105-12-S9-S17

In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations, where genomes allow a mix of linear and circular chromosomes to be present. First, we formulate an equivalent optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in a breakpoint graph. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than l can be reduced to the well-known degree-bounded k-set packing problem with k = 2l. Finally, a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by double-cut-and-join operations is devised, which achieves the approximation ratio 13/9 + epsilon approximate to 1.4444 + epsilon, for any positive epsilon. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved to 69/49 + epsilon approximate to 1.4082 + epsilon.

• 出版日期2011-10-5
• 单位南阳理工学院