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Finding All Common Intervals of k Permutations

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Book cover Combinatorial Pattern Matching (CPM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2089))

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Abstract

Given k permutations of n elements, a k-tuple of intervals of these permutations consisting of the same set of elements is called a common interval. We present an algorithm that finds in a family of k permutations of n elements all K common intervals in optimal O(nk+K) time and O(n) additional space.

This extends a result by Uno and Yagiura (Algorithmica 26, 290-309, 2000) who present an algorithm to find all K common intervals of k = 2 permutations in optimal O(n+K) time and O(n) space. To achieve our result, we introduce the set of irreducible intervals, a generating subset of the set of all common intervals of k permutations.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. R.M. Brady. Optimization strategies gleaned from biological evolution. Nature, 317:804–806, 1985.

    Article  Google Scholar 

  3. D. Fulkerson and O. Gross. Incidence matrices with the consecutive 1s property. Bull. Am. Math. Soc., 70:681–684, 1964.

    Article  MathSciNet  MATH  Google Scholar 

  4. M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.

    MATH  Google Scholar 

  5. S. Kobayashi, I. Ono, and M. Yamamura. An efficient genetic algorithm for job shop scheduling problems. In Proc. of the 6th International Conference on Genetic Algorithms, pages 506–511. Morgan Kaufmann, 1995.

    Google Scholar 

  6. E.M. Marcotte, M. Pellegrini, H.L. Ng, D.W. Rice, T.O. Yeates, and D. Eisenberg. Detecting protein function and protein-protein interactions from genome sequences. Science, 285:751–753, 1999.

    Article  Google Scholar 

  7. H. Mühlenbein, M. Gorges-Schleuter, and O. Krämer. Evolution algorithms in combinatorial optimization. Parallel Comput., 7:65–85, 1988.

    Article  MATH  Google Scholar 

  8. R. Overbeek, M. Fonstein, M. D’Souza, G.D. Pusch, and N. Maltsev. The use of gene clusters to infer functional coupling. Proc. Natl. Acad. Sci. USA, 96(6):2896–2901, 1999.

    Article  Google Scholar 

  9. B. Snel, G. Lehmann, P. Bork, and M.A. Huynen. STRING: A web-server to retrieve and display the repeatedly occurring neigbourhood of a gene. Nucleic Acids Res., 28(18):3443–3444, 2000.

    Article  Google Scholar 

  10. T. Uno and M. Yagiura. Fast algorithms to enumerate all common intervals of two permutations. Algorithmica, 26(2):290–309, 2000.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretical Bioinformatics, Heidelberg, Germany

    Steffen Heber & Jens Stoye

  2. Functional Genome Analysis (H0800) German Cancer Research Center (DKFZ), Heidelberg, Germany

    Steffen Heber

Authors
  1. Steffen Heber
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  2. Jens Stoye
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel, Atlanta, Georgia, 30332-0280, USA

    Amihood Amir

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© 2001 Springer-Verlag Berlin Heidelberg

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Heber, S., Stoye, J. (2001). Finding All Common Intervals of k Permutations. In: Amir, A. (eds) Combinatorial Pattern Matching. CPM 2001. Lecture Notes in Computer Science, vol 2089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48194-X_19

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  • DOI: https://doi.org/10.1007/3-540-48194-X_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42271-6

  • Online ISBN: 978-3-540-48194-2

  • eBook Packages: Springer Book Archive

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