Skip to main content
SpringerLink
Log in

Two-Interval Pattern Problems

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 62 Accesses

Years and Authors of Summarized Original Work

  • 2004; Vialette

  • 2007; Cheng, Yang, Yuan

Problem Definition

The problem is concerned with finding large constrained patterns in sets of 2-intervals. Given a single‐stranded RNA molecule, a sequence of contiguous bases of the molecule can be represented as an interval on a single line, and a possible pairing between two disjoint sequences can be represented as a 2-interval, which is merely the union of two disjoint intervals. Derived from arc‐annotated sequences, 2-interval representation considers thus only the bonds between the bases and the pattern of the bonds, such as hairpin structures, knots and pseudoknots. A maximum cardinality disjoint subset of a candidate set of 2-intervals restricted to certain prespecified geometrical constraints can provide a useful valid approximation for RNA secondary structure determination.

The geometric properties of 2-intervals provide a possible guide for understanding the computational complexity of...

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 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover 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

Recommended Reading

  1. Bar-Yehuda R, Halldorsson M, Naor J, Shachnai H, Shapira I (2002) Scheduling split intervals. In: Proceedings of the 13th annual ACM-SIAM symposium on discrete algorithms (SODA), pp 732–741

    Google Scholar 

  2. Billoud B, Kontic M, Viari A (1996) Palingol a declarative programming language to describe nucleic acids' secondary structures and to scan sequence database. Nucleic Acids Res 24:1395–1403

    Article  Google Scholar 

  3. Blin G, Fertin G, Vialette S (2007) Extracting 2-intervals subsets from 2-interval sets. Theor Comput Sci 385(1–3):241–263

    Article  MathSciNet  MATH  Google Scholar 

  4. Blin G, Fertin G, Vialette S (2004) New results for the 2-interval pattern problem. In: Proceedings of the 15th annual symposium on combinatorial pattern matching (CPM). Lecture notes in computer science, vol 3109. Springer, Berlin

    Google Scholar 

  5. Butman A, Hermelin D, Lewenstein M, Rawitz D (2007) Optimization problems in multiple-interval graphs. In: Proceedings of the 9th annual ACM-SIAM symposium on discrete algorithms (SODA), ACM-SIAM 2007, pp 268–277

    Google Scholar 

  6. Chen J-H, Le S-Y, Maize J (2000) Prediction of common secondary structures of RNAs: a genetic algorithm approach. Nucleic Acids Res 28:991–999

    Article  Google Scholar 

  7. Crochemore M, Hermelin D, Landau G, Rawitz D, Vialette S (2008) Approximating the 2-interval pattern problem. Theor Comput Sci (special issue for Alberto Apostolico)

    Google Scholar 

  8. Erdong C, Linji Y, Hao Y (2007) Improved algorithms for 2-interval pattern problem. J Comb Optim 13(3):263–275

    Article  MathSciNet  MATH  Google Scholar 

  9. Halldorsson M, Karlsson R (2006) Strip graphs: recognition and scheduling. In: Proceedings of the 32nd international workshop on graph-theoretic concepts in computer science (WG). Lecture notes in computer science, vol 4271. Springer, Berlin, pp137–146

    Google Scholar 

  10. Jiang M (2007) A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. J Comb Optim 13:217–221

    Article  MathSciNet  MATH  Google Scholar 

  11. Jiang M (2007) Improved approximation algorithms for predicting RNA secondary structures with arbitrary pseudoknots. In: Proceedings of the 3rd international conference on algorithmic aspects in information and management (AAIM), Portland. Lecture notes in computer science, vol 4508. Springer, pp 399–410

    Google Scholar 

  12. Jiang M (2007) A PTAS for the weighted 2-interval pattern problem over the preceding-and-crossing model. In: Xu Y, Dress AWM, Zhu B (eds) Proceedings of the 1st annual international conference on combinatorial optimization and applications (COCOA), Xi'an. Lecture notes in computer science, vol 4616. Springer, pp 378–387

    Google Scholar 

  13. Joseph D, Meidanis J, Tiwari P (1992) Determining DNA sequence similarity using maximum independent set algorithms for interval graphs. In: Proceedings of the 3rd Scandinavian workshop on algorithm theory (SWAT). Lecture notes in computer science. Springer, Berlin, pp 326–337

    Google Scholar 

  14. Lyngsø R, Pedersen C: RNA pseudoknot prediction in energy-based models. J Comput Biol 7:409–427 (2000)

    Google Scholar 

  15. Micali S, Vazirani V (1980) An O(sqrt|V||E|) algorithm for finding maximum matching in general graphs. In: Proceedings of the 21st annual symposium on foundation of computer science (FOCS). IEEE, pp 17–27

    Google Scholar 

  16. Nussinov R, Pieczenik G, Griggs J, Kleitman D (1978) Algorithms for loop matchings. SIAM J Appl Math 35:68–82

    Google Scholar 

  17. Ren J, Rastegart B, Condon A, Hoos H (2005) HotKnots: heuristic prediction of rna secondary structure including pseudoknots. RNA 11:1194–1504

    Google Scholar 

  18. Rivas E, Eddy S (1999) A dynamic programming algorithm for RNA structure prediction including pseudoknots. J Mol Biol 285:2053–2068

    Google Scholar 

  19. Ruan J, Stormo G, Zhang W (2004) An iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots. Bioinformatics 20:58–66

    Google Scholar 

  20. Vialette S (2004) On the computational complexity of 2-interval pattern matching. Theor Comput Sci 312:223–249

    Google Scholar 

  21. Zhao J, Malmberg R, Cai L (2006) Rapid ab initio RNA folding including pseudoknots via graph tree decomposition. In: Proceedings of the workshop on algorithms in bioinformatics. Lecture notes in computer science, vol 4175. Springer, Berlin, pp 262–273

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IGM-LabInfo, University of Paris-East, Descartes, France

    Stéphane Vialette

Authors
  1. Stéphane Vialette
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Vialette, S. (2016). Two-Interval Pattern Problems. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_445

Download citation

Publish with us

Policies and ethics

Search

Navigation