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

• Main Authors: Yu Jiadong, Sun Ruimin, Chen Xin
• Format: Article
• Language: English
• Published: BMC 2011-10-01
• Series: BMC Bioinformatics
• Online Access: http://www.biomedcentral.com/1471-2105/12/S9/S17

<p>Abstract</p> <p>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 <it>l</it> can be reduced to the well-known degree-bounded <it>k</it>-set packing problem with <it>k</it> = 2<it>l.</it> 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 <inline-formula><graphic file="1471-2105-12-S9-S17-i1.gif"/></inline-formula> for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved to <inline-formula><graphic file="1471-2105-12-S9-S17-i2.gif"/></inline-formula></p>