A 1.375-approximation algorithm for sorting by transpositions

  • Authors:

  • Isaac Elias;Tzvika Hartman

  • Affiliations:

  • Dept. of Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm, Sweden;Dept. of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel

  • Venue:
  • WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
  • Year:
  • 2005

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Abstract

Sorting permutations by transpositions is an important problem in genome rearrangements. A transposition is a rearrangement operation in which a segment is cut out of the permutation and pasted in a different location. The complexity of this problem is still open and it has been a ten-year-old open problem to improve the best known 1.5-approximation algorithm. In this paper we provide a 1.375-approximation algorithm for sorting by transpositions. The algorithm is based on a new upper bound on the diameter of 3-permutations. In addition, we present some new results regarding the transposition diameter: We improve the lower bound for the transposition diameter of the symmetric group, and determine the exact transposition diameter of 2-permutations and simple permutations.