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Sorting with Forbidden Intermediates

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Algorithms for Computational Biology (AlCoB 2016)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9702))

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Abstract

A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are useful for instance when reconstructing potential scenarios of evolution between species, or when trying to assess their similarity. We revisit those problems by adding a new constraint on the sequences to be computed: they must avoid a given set of forbidden intermediates, which correspond to species that cannot exist because the mutations that would be involved in their creation are lethal. We initiate this study by focusing on the case where the only mutations that can occur are exchanges of any two elements in the permutations, and give a polynomial time algorithm for solving that problem when the permutation to sort is an involution.

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Notes

  1. 1.

    See [3], Appendix B2 for correctness and Appendix B3 for complexity.

  2. 2.

    See [3], Appendix B2-B3 for proofs of correctness and complexity.

  3. 3.

    See [3], Appendix B2 for correctness.

  4. 4.

    See [3], Appendix B2.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Carlo Comin

  2. Université Paris-Est, LIGM (UMR 8049), UPEM, CNRS, ESIEE, ENPC, 77454, Marne-la-Vallée, France

    Carlo Comin, Anthony Labarre & Stéphane Vialette

  3. Department of Computer Science, University of Verona, Verona, Italy

    Romeo Rizzi

Authors
  1. Carlo Comin
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  2. Anthony Labarre
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  3. Romeo Rizzi
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  4. Stéphane Vialette
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Correspondence to Carlo Comin .

Editor information

Editors and Affiliations

  1. CETA-Ciemat, Trujillo, Spain

    María Botón-Fernández

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Extremadura, Cáceres, Spain

    Sergio Santander-Jiménez

  4. University of Extremadura, Cáceres, Spain

    Miguel A. Vega-Rodríguez

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© 2016 Springer International Publishing Switzerland

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Comin, C., Labarre, A., Rizzi, R., Vialette, S. (2016). Sorting with Forbidden Intermediates. In: Botón-Fernández, M., Martín-Vide, C., Santander-Jiménez, S., Vega-Rodríguez, M.A. (eds) Algorithms for Computational Biology. AlCoB 2016. Lecture Notes in Computer Science(), vol 9702. Springer, Cham. https://doi.org/10.1007/978-3-319-38827-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-38827-4_11

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  • Print ISBN: 978-3-319-38826-7

  • Online ISBN: 978-3-319-38827-4

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