Abstract
Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we design a new 1.375-algorithm for the MIN-SBR problem.
Most proofs are omitted in this extended abstract. The full version with complete proofs is available at ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/ 2001/TR01-047.
Research done in part while visiting Dept. of Computer Science, University of Bonn. Work partially supported by NSF grant CCR-9700053, NIH grant 9R01HG02238-12 and DFG grant Bo 56/157-1.
Research done in part while vising Dept. of Computer Science, Princeton University. Work partially supported by DFG grants, DIMACS, and IST grant 14036 (RAND-APX).
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Berman, P., Hannenhalli, S., Karpinski, M. (2002). 1.375-Approximation Algorithm for Sorting by Reversals. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_21
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DOI: https://doi.org/10.1007/3-540-45749-6_21
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