A (1.408+ε)-approximation algorithm for sorting unsigned genomes by reciprocal translocations

Abstract

Sorting genomes by translocations is a classic combinatorial problem in genome rearrangements. The translocation distance for signed genomes can be computed exactly in polynomial time, but for unsigned genomes the problem becomes NP-Hard and the current best approximation ratio is 1.5+ε. In this paper, we investigate the problem of sorting unsigned genomes by translocations. Firstly, we propose a tighter lower bound of the optimal solution by analyzing some special sub-permutations; then, by exploiting the two well-known algorithms for approximating the maximum independent set on graphs with a bounded degree and for set packing with sets of bounded size, we devise a new polynomial-time approximation algorithm, improving the approximation ratio to 1.408+ε, where ε = O(1/logn). © 2014 Springer International Publishing.