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Sorting by Prefix Transpositions

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String Processing and Information Retrieval (SPIRE 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2476))

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Abstract

A transposition is an operation that exchanges two consecutive, adjacent blocks in a permutation. A prefix transposition is a transposition that moves the first element in the permutation. In this work we present the first results on the problem of sorting permutations with the minimum number of prefix transpositions. This problem is a variation of the transposition distance problem, related to genome rearrangements. We present approximation algorithms with performance ratios of 2 and 3. We conjecture that the maximum prefix transposition distance is D(n) = n— ⌊n/4 ⌋ and present the results of several computational tests that support this. Finally, we propose an algorithm that decides whether a given permutation can be sorted using just the number of transpositions indicated by the breakpoint lower-bound.

Research supported by FAPESP

Research supported in part by CNPq and FAPESP

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Author information

Authors and Affiliations

  1. Institute of Computing, University of Campinas, P.O.Box 6167, 13084-971, Campinas, Brazil

    Zanoni Dias & João Meidanis

Authors
  1. Zanoni Dias
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  2. João Meidanis
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Editor information

Editors and Affiliations

  1. Departamento de Ciěncia da Computação, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, MG, Brazil

    Alberto H. F. Laender

  2. Instituto Superior Técnico, INESC-ID, R. Alves Redol 9, 1000-029, Lisboa, Portugal

    Arlindo L. Oliveira

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© 2002 Springer-Verlag Berlin Heidelberg

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Dias, Z., Meidanis, J. (2002). Sorting by Prefix Transpositions. In: Laender, A.H.F., Oliveira, A.L. (eds) String Processing and Information Retrieval. SPIRE 2002. Lecture Notes in Computer Science, vol 2476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45735-6_7

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  • DOI: https://doi.org/10.1007/3-540-45735-6_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44158-8

  • Online ISBN: 978-3-540-45735-0

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