Skip to main content
SpringerLink
Log in

On the Complexity of Scaffolding Problems: From Cliques to Sparse Graphs

  • Conference paper
  • First Online:
Combinatorial Optimization and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9486))

Abstract

This paper is devoted to new results about the scaffolding problem, an integral problem of genome inference in bioinformatics. The problem consists of finding a collection of disjoint cycles and paths covering a particular graph called the “scaffold graph”. We examine the difficulty and the approximability of the scaffolding problem in special classes of graphs, either close to trees, or very dense. We propose negative and positive results, exploring the frontier between difficulty and tractability of computing and/or approximating a solution to the problem.

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 EPUB and 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

Notes

  1. 1.

    available on http://www.lirmm.fr/~chateau/proof_cocoa_2015.pdf.

  2. 2.

    That is, Algorithm 1 produces a solution of weight at least half the optimum weight.

  3. 3.

    The ETH states: there is a constant \(c >1\) such that no \(O(c^n)\)-time algorithm for n-variable 3-SAT exists.

References

  1. Alimonti, P., Ausiello, G., Giovaniello, L., Protasi, M.: On the complexity of approximating weighted satisfiability problems. Technical report, Università degli Studi di Roma La Sapienza. Rapporto Tecnico RAP 38.97 (1997)

    Google Scholar 

  2. Brandstädt, A.: Partitions of graphs into one or two independent sets and cliques. Discrete Math. 152(1–3), 47–54 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chateau, A., Giroudeau, R.: Complexity and polynomial-time approximation algorithms around the scaffolding problem. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) AlCoB 2014. LNCS, vol. 8542, pp. 47–58. Springer, Heidelberg (2014)

    Google Scholar 

  4. Chateau, A., Giroudeau, R.: A complexity and approximation framework for the maximization scaffolding problem. Theor. Comput. Sci. 595, 92–106 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D.W., Kanj, I.A., Xia, G.: Tight lower bounds for certain parameterized NP-hard problems. Inf. Comput. 201(2), 216–231 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Crescenzi, P.: A short guide to approximation preserving reductions. In: Proceedings of the Twelfth Annual IEEE Conference on Computational Complexity, Ulm, Germany, June 24–27, 1997, pp. 262–273 (1997)

    Google Scholar 

  7. Dayarian, A., Michael, T., Sengupta, A.: SOPRA: scaffolding algorithm for paired reads via statistical optimization. BMC Bioinform. 11, 345 (2010)

    Article  Google Scholar 

  8. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, London (2013)

    Book  MATH  Google Scholar 

  9. Gao, S., Sung, W.-K., Nagarajan, N.: Opera: reconstructing optimal genomic scaffolds with high-throughput paired-end sequences. J. Comput. Biol. 18(11), 1681–1691 (2011)

    Article  MathSciNet  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness (1979)

    Google Scholar 

  11. Håstad, J.: Clique is hard to approximate within \(n^{1-\varepsilon }\). Electron. Colloquium Comput. Complex. (ECCC) 4(38) (1997)

    Google Scholar 

  12. Hunt, M., Newbold, C., Berriman, M., Otto, T.: A comprehensive evaluation of assembly scaffolding tools. Genome Biol. 15(3), R42 (2014)

    Article  Google Scholar 

  13. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? J. Comput. Syst. Sci. 63(4), 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lokshtanov, D., Marx, D., Saurabh, S.: Lower bounds based on the exponential time hypothesis. Bull. EATCS 105, 41–72 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Weller, M., Chateau, A., Giroudeau, R.: Exact approaches for scaffolding. Accepted in RECOMBCG 2015, to appear in BMC Bioinformatics 2015a

    Google Scholar 

  16. Weller, M., Chateau, A., Giroudeau, R.: On the implementation of polynomial-time approximation algorithms for scaffold problems. Technical report (2015)

    Google Scholar 

  17. Woeginger, G.: Exact algorithms for NP-hard problems: a survey. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds.) Combinatorial Optimization — Eureka, You Shrink!. LNCS, vol. 2570, pp. 185–207. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIRMM - CNRS UMR 5506, Montpellier, France

    Mathias Weller, Annie Chateau & Rodolphe Giroudeau

  2. IBC, Montpellier, France

    Mathias Weller & Annie Chateau

Authors
  1. Mathias Weller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Annie Chateau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rodolphe Giroudeau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Annie Chateau .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Marywood University, Scranton, Pennsylvania, USA

    Zaixin Lu

  2. North Carolina Central University, Durham, North Carolina, USA

    Donghyun Kim

  3. University of Texas at Dallas, Richardson, Texas, USA

    Weili Wu

  4. Texas Southern University, Houston, Texas, USA

    Wei Li

  5. University of Texas at Dallas, Richardson, Texas, USA

    Ding-Zhu Du

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Weller, M., Chateau, A., Giroudeau, R. (2015). On the Complexity of Scaffolding Problems: From Cliques to Sparse Graphs. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26626-8_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26625-1

  • Online ISBN: 978-3-319-26626-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation