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+e. 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+e, where e = O(1/logn).
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