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A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions

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Book cover Combinatorial Pattern Matching (CPM 2003)

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Abstract

An important problem in genome rearrangements is sorting permutations by transpositions. Its complexity is still open, and two rather complicated 1.5-approximation algorithms for sorting linear permutations are known (Bafna and Pevzner, 96 and Christie, 98). In this paper, we observe that the problem of sorting circular permutations by transpositions is equivalent to the problem of sorting linear permutations by transpositions. Hence, all algorithms for sorting linear permutations by transpositions can be used to sort circular permutations. Our main result is a new 1.5-approximation algorithm, which is considerably simpler than the previous ones, and achieves running time which is equal to the best known. Moreover, the analysis of the algorithm is significantly less involved, and provides a good starting point for studying related open problems.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Tzvika Hartman

Authors
  1. Tzvika Hartman
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Editors and Affiliations

  1. Depto. de Ciencias de la Computación, Universidad de Chile, Blanco Encalada 2120, Santiago, 6511224, Chile

    Ricardo Baeza-Yates

  2. Escuela de Ciencias Físico-Matemáticas, Universidad Michoacana, Edificio “B”, ciudad universitaria, Morelia Michoacán, Mexico

    Edgar Chávez

  3. Université de Marne-la-Vallée, 77454, Marne-la-Vallée Cedex 2, France

    Maxime Crochemore

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© 2003 Springer-Verlag Berlin Heidelberg

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Hartman, T. (2003). A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds) Combinatorial Pattern Matching. CPM 2003. Lecture Notes in Computer Science, vol 2676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44888-8_12

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  • DOI: https://doi.org/10.1007/3-540-44888-8_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40311-1

  • Online ISBN: 978-3-540-44888-4

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