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

• Main Authors: Chen, Xin, Sun, Ruimin, Yu, Jiadong
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: Mathematical Sciences
• Online Access: https://hdl.handle.net/10356/100350; http://hdl.handle.net/10220/17879
• Institution: Nanyang Technological University

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 + e ≈ 1.4444 + e, for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved to 69/49 + e ≈ 1.4082 + e.