Skip to main content

Tractability Results for the Consecutive-Ones Property with Multiplicity

  • Conference paper
Combinatorial Pattern Matching (CPM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6661))

Included in the following conference series:

  • 1047 Accesses

Abstract

A binary matrix has the Consecutive-Ones Property (C1P) if its columns can be ordered in such a way that all 1’s in each row are consecutive. We consider here a variant of the C1P where columns can appear multiple times in the ordering. Although the general problem of deciding the C1P with multiplicity is NP-complete, we present here a case of interest in comparative genomics that is tractable.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adam, Z., Turmel, M., Lemieux, C., Sankoff, D.: Common intervals and symmetric difference in a model-free phylogenomics, with an application to streptophyte evolution. J. Comput. Biol. 14, 436–445 (2007)

    Article  MathSciNet  Google Scholar 

  2. Alizadeh, F., Karp, R., Weisser, D., Zweig, G.: Physical mapping of chromosomes using unique probes. J. Comput. Biol. 2, 159–184 (1995)

    Article  MATH  Google Scholar 

  3. Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity. J. Comput. Syst. Sci. 13, 335–379 (1976)

    Article  MATH  Google Scholar 

  4. Chauve, C., Tannier, E.: A methodological framework for the reconstruction of contiguous regions of ancestral genomes and its application to mammalian genome. PLoS Comput. Biol. 4, paper e1000234 (2008)

    Google Scholar 

  5. Habib, M., McConnell, R.M., Paul, C., Viennot, L.: Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing. Theoret. Comput. Sci. 234, 59–84 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Landau, G.M., Parida, L., Weimann, O.: Gene proximity analysis across whole genomes via PQ trees. J. Comput. Biol. 12, 1289–1306 (2005)

    Article  Google Scholar 

  7. Lu, W.-F., Hsu, W.-L.: A test for the Consecutive Ones Property on noisy data – application to physical mapping and sequence assembly. J. Comput. Biol. 10, 709–735 (2003)

    Article  Google Scholar 

  8. Ma, J., Zhang, L., Suh, B.B., Raney, B.J., Burhans, R.C., Kent, W.J., Blanchette, M., Haussler, D., Miller, W.: Reconstructing contiguous regions of an ancestral genome. Genome Res. 16, 1557–1565 (2006)

    Article  Google Scholar 

  9. McConnell, R.M.: A certifying algorithm for the consecutive-ones property. In: SODA 2004, pp. 761–770. ACM, New York (2004)

    Google Scholar 

  10. Meidanis, J., Porto, O., Telles, G.P.: On the consecutive ones property. Discrete Appl. Math. 88, 325–354 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hsu, W.-L.: A simple test for the Consecutive Ones Property. J. Algorithms 43, 1–16 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wittler, R., Stoye, J.: Consistency of sequence-based gene clusters. In: Tannier, E. (ed.) RECOMB-CG 2010. LNCS, vol. 6398, pp. 252–263. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Wittler, R., Maňuch, J., Patterson, M., Stoye, J.: Consistency of sequence-based gene clusters (unpublished manuscript)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chauve, C., Maňuch, J., Patterson, M., Wittler, R. (2011). Tractability Results for the Consecutive-Ones Property with Multiplicity. In: Giancarlo, R., Manzini, G. (eds) Combinatorial Pattern Matching. CPM 2011. Lecture Notes in Computer Science, vol 6661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21458-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21458-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21457-8

  • Online ISBN: 978-3-642-21458-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics