Advertisement

Finding All Common Intervals of k Permutations

  • Steffen Heber
  • Jens Stoye
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2089)

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.

Keywords

Standard Notation Maximal Chain Single Machine Schedule Problem Additional Space Active Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    R.M. Brady. Optimization strategies gleaned from biological evolution. Nature, 317:804–806, 1985.CrossRefGoogle Scholar
  3. 3.
    D. Fulkerson and O. Gross. Incidence matrices with the consecutive 1s property. Bull. Am. Math. Soc., 70:681–684, 1964.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.zbMATHGoogle Scholar
  5. 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. 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.CrossRefGoogle Scholar
  7. 7.
    H. Mühlenbein, M. Gorges-Schleuter, and O. Krämer. Evolution algorithms in combinatorial optimization. Parallel Comput., 7:65–85, 1988.zbMATHCrossRefGoogle Scholar
  8. 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.CrossRefGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. 10.
    T. Uno and M. Yagiura. Fast algorithms to enumerate all common intervals of two permutations. Algorithmica, 26(2):290–309, 2000.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Steffen Heber
    • 1
    • 2
  • Jens Stoye
    • 1
  1. 1.Theoretical BioinformaticsHeidelbergGermany
  2. 2.Functional Genome Analysis (H0800) German Cancer Research Center (DKFZ)HeidelbergGermany

Personalised recommendations