Skip to main content
SpringerLink
Log in
Book cover

International Conference on Bioinformatics and Biomedical Engineering

IWBBIO 2015: Bioinformatics and Biomedical Engineering pp 491–502Cite as

A Unified Integer Programming Model for Genome Rearrangement Problems

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9043))

Abstract

We describe an integer programming (IP) model that can be applied to the solution of all genome-rearrangement problems in the literature. No direct IP model for such problems had ever been proposed prior to this work. Our model employs an exponential number of variables, but it can be solved by column generation techniques. I.e., we start with a small number of variables and we show how the correct missing variables can be added to the model in polynomial time.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bader, M., Ohlebusch, E.: Sorting by weighted reversals, transpositions, and inverted transpositions. J. Comput. Biol. 14, 615–636 (2007)

    Article  MathSciNet  Google Scholar 

  2. Bafna, V., Pevzner, P.: Genome rearrangements and sorting by reversals. SIAM J. Comp. 25, 272–289 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bafna, V., Pevzner, P.: Sorting by transpositions. SIAM J. Discr. Math. 11, 224–240 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W., Vance, P.H.: Branch-and-Price: Column Generation for Solving Huge Integer Programs. Op. Res. 46, 316–329 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Berman, P., Hannenhalli, S., Karpinski, M.: 1.375-Approximation algorithm for sorting by reversals. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 200–210. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Bulteau, L., Fertin, G., Rusu, I.: Pancake Flipping is Hard. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 247–258. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Bulteau, L., Fertin, G., Rusu, I.: Sorting by Transpositions Is Difficult. SIAM J. Discr. Math. 26, 1148

    Google Scholar 

  8. Caprara, A.: Sorting by reversals is difficult. In: 1st ACM/IEEE International Conference on Computational Molecular Biology, pp. 75–83. ACM Press (1997)

    Google Scholar 

  9. Caprara, A.: Sorting Permutations by Reversals and Eulerian Cycle Decompositions. SIAM J. on Disc. Math. 12, 91–110 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Caprara, A., Lancia, G., Ng, S.-K.: A Column-Generation Based Branch-and-Bound Algorithm for Sorting By Reversals. In: Mathematical Support For Molecular Biology. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 47, pp. 213–226 (1999)

    Google Scholar 

  11. Caprara, L.G., Ng, S.K.: Sorting Permutations by Reversals through Branch and Price. INFORMS J. on Comp. 13, 224–244 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chitturi, B., Fahle, W., Meng, Z., Morales, L., Shields, C.O., Sudborough, I.H., Voit, W.: An 18/11 n upper bound for sorting by prefix reversals. Theor. Comp. Sc. 410, 3372–3390 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Christie, A.: A 3/2-approximation algorithm for sorting by reversals. In: 9th ACM-SIAM Symposium on Discrete Algorithms, pp. 244–252. ACM Press (1998)

    Google Scholar 

  14. Fischer, J., Ginzinger, S.W.: A 2-Approximation Algorithm for Sorting by Prefix Reversals. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 415–425. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Gates, W., Papadimitriou, C.: Bounds for sorting by prefix reversal. Discr. Math. 27, 47–57 (1979)

    Article  MathSciNet  Google Scholar 

  16. Gu, Q.P., Peng, S., Sudborough, H.: A 2-approximation algorithm for genome rearrangements by reversals and transpositions. Theoret. Comput. Sci. 210, 327–339 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hartman, T., Sharan, R.: A 1.5-approximation algorithm for sorting by transpositions and transreversals. J. Comput. Syst. Sci. 70, 300–320 (2005)

    Google Scholar 

  18. Kececioglu, J., Sankoff, D.: Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement. Algorithmica 13, 180–210 (1995)

    Google Scholar 

  19. Lancia, G., Serafini, P.: Deriving compact extended formulations via LP-based separation techniques. 4OR 12, 201–234 (2014)

    Google Scholar 

  20. Meidanis, J., Walter, M.M.T., Dias, Z.: A Lower Bound on the Reversal and Transposition Diameter. J. Comput. Biol. 9, 743–745 (2002)

    Article  Google Scholar 

  21. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization, 784 pages. Wiley (1999)

    Google Scholar 

  22. Sankoff, D., Cedergren, R., Abel, Y.: Genomic divergence through gene rearrangement. In: Molecular Evolution: Computer Analysis of Protein and Nucleic Acid Sequences, pp. 428–438. Academic Press, New York (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Udine, Via delle Scienze 206, 33100, Udine, Italy

    Giuseppe Lancia, Franca Rinaldi & Paolo Serafini

Authors
  1. Giuseppe Lancia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Franca Rinaldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Serafini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dpto. de Arquitectura y Tecnología de Computadores (ATC)., E.T.S. de Ingenierías en Informática y Telecomunicación. CITIC-UGR, Universidad de Granada, c/ Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Francisco Ortuño

  2. E.T.S. Ingenierías Informática y de Telecomunicación , , Dpto. Arquitectura y Tecnología de Computadores, CITIC-UGR, Universidad de Granada, C Periodista Rafael Gómez Montero, 18071, Granada, Spain

    Ignacio Rojas

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Lancia, G., Rinaldi, F., Serafini, P. (2015). A Unified Integer Programming Model for Genome Rearrangement Problems. In: Ortuño, F., Rojas, I. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2015. Lecture Notes in Computer Science(), vol 9043. Springer, Cham. https://doi.org/10.1007/978-3-319-16483-0_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16483-0_48

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16482-3

  • Online ISBN: 978-3-319-16483-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation