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)


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.


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.


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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

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