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).
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Jiang, H., Wang, L., Zhu, B., Zhu, D. (2014). A (1.408+ε)-Approximation Algorithm for Sorting Unsigned Genomes by Reciprocal Translocations. In: Chen, J., Hopcroft, J.E., Wang, J. (eds) Frontiers in Algorithmics. FAW 2014. Lecture Notes in Computer Science, vol 8497. Springer, Cham. https://doi.org/10.1007/978-3-319-08016-1_12
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DOI: https://doi.org/10.1007/978-3-319-08016-1_12
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