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This article is part of the supplement: Proceedings of the Ninth Annual Research in Computational Molecular Biology (RECOMB) Satellite Workshop on Comparative Genomics

Open Access Proceedings

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

Xin Chen*, Ruimin Sun and Jiadong Yu

Author Affiliations

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

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BMC Bioinformatics 2011, 12(Suppl 9):S17  doi:10.1186/1471-2105-12-S9-S17

Published: 5 October 2011

Abstract

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 for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved to