Skip to main content
SpringerLink
Log in

Physical Mapping with Repeated Probes: The Hypergraph Superstring Problem

  • Conference paper
  • First Online:
Combinatorial Pattern Matching (CPM 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1645))

Included in the following conference series:

Abstract

We focus on the combinatorial analysis of physical mapping with repeated probes. We present computational complexity results, and we describe and analyze an algorithmic strategy. We are following the research avenue proposed by Karp [9] on modeling the problem as a combinatorial problem - the Hypergraph Superstring Problem - intimately related to the Lander-Waterman stochastic model [16]. We show that a sparse version of the problem is MAXSNP-complete, a result that carries over to the general case. We show that the minimum Sperner decomposition of a set collection, a problem that is related to the Hypergraph Superstring problem, is NP-complete. Finally we show that the Generalized Hypergraph Superstring Problem is also MAXSNP-hard.We present an efficient algorithm for retrieving the PQ-tree of optimal zero repetition solutions, that provides a constant approximation to the optimal solution on sparse data. We provide experimental results on simulated data.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Papadimitriou C.H. Approximability. In Computational Complexity. Addison-Wesley Publishing Company, 1994.

    Google Scholar 

  2. Papadimitriou C.H. and Yannakakis M. The traveling salesman problem with distances one and two. Math. of Operations Research, pages 1–12, 1993.

    Google Scholar 

  3. Green E.D. and Green P. Sequence-tagged site (sts) content mapping of human chromosomes: Theoretical considerations and early experiences. PCR Methods and Applications, 1:77–90, 1991.

    Article  Google Scholar 

  4. Greenberg D.S. and Istrail S. Physical mapping by sts hybridization: Algorithmic strategiews and the challange of software evaluation. Journal of Computational Biology, 2, Number 2:219–274, 1995.

    Article  Google Scholar 

  5. Lander E.S. and Waterman M.S. Genomic mapping by fingerprinting random clones: A mathematical analysis. Genomics, 2:231–239, 1988.

    Article  Google Scholar 

  6. Alizadeh F., Karp M.R., Newberg L.A., and Weisser D.K. Physical mapping of chromosomes: A combinatorial problem in molecular biology. Algorithmica, 13:52–76, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  7. Alizadeh F., Karp R.M., Weisser D.K., and Zweig G. Physical mapping of chromosomes using unique probes. Manuscript, 1995.

    Google Scholar 

  8. Lipski W. Jr. On strings containing all subsets as substrings. Discrete Mathematics, 21:253–259, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  9. Karp R.M. Mapping the genome: Some combinatorial problems arising in molecular biology. Symposium on Discrete Algorithms, SODA 93:278–285, 1993.

    Google Scholar 

  10. Waterman M.S. Personal communication about the work of Simon Tavare. Ocrober, 1997.

    Google Scholar 

  11. Nelson D.O. and Speed T.P. Statistical issues in constructing high resolution physical maps. Statistical Science, 9, No. 3:334–354, 1994.

    Article  Google Scholar 

  12. Erdos Paul. Personal Communication, 1993.

    Google Scholar 

  13. Arratia R., Lander E.S., Tavare S., and Waterman M.S. Genomic mapping by anchoring random clones: A mathematical analysis. Genomics, 11:806–827, 1991.

    Article  Google Scholar 

  14. Booth K.S. and Lueker G.S. Testing for the consecutive ones property, interval graphs and planarity using pq-tree algorithms. J. Comput. Sys. Sci., 13:335–379, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  15. Foote S., Vollrath D., Hilton A., and Page D. The human y chromosome: Overlapping dna clones spanning the euchromatic region. Science, pages 60–66, October 1992.

    Google Scholar 

  16. Lander E.S. and Waterman M.S. Genomic mapping by fingerprinting random clones: A mathematical analysis. Genomics, 2, Number 2:219–274, 1988.

    Google Scholar 

  17. Waterman M.S. In Introduction to Computational Biology. Chapman and Hall, 1995.

    Google Scholar 

  18. Shamir. Personal communication, October 1997.

    Google Scholar 

  19. Ghosh S.P. Consecutive storage of relevant records with redundancy. Communications of the ACM, 18:464–471, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  20. Kou A.T. Polynomial complete consecutive information retrieval problems. SIAM J. Computing, 6, No.1:67–75, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  21. Lipski W. Information storage and retrieval-mathematical foundations ii. Theoretical Computer Science, 3:183–212, 1976.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MIT Laboratory for Computer Science, Cambridge, MA, 02139, USA

    Serafim Batzoglou

  2. Massively Parallel Computer Research Lab MS1110, Sandia National Laboratories, Albuquerque, NM 87185-1110, USA

    Sorin Istrail

Authors
  1. Serafim Batzoglou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sorin Istrail
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute Gaspard-Monge, University of Marne-la-Vallée, F 77454, Marne-la-Vallée Cedex 2, France

    Maxime Crochemore

  2. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, England

    Mike Paterson

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Batzoglou, S., Istrail, S. (1999). Physical Mapping with Repeated Probes: The Hypergraph Superstring Problem. In: Crochemore, M., Paterson, M. (eds) Combinatorial Pattern Matching. CPM 1999. Lecture Notes in Computer Science, vol 1645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48452-3_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-48452-3_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66278-5

  • Online ISBN: 978-3-540-48452-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation