Finding Nested Common Intervals Efficiently

  • Guillaume Blin
  • Jens Stoye
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5817)


In this paper, we study the problem of efficiently finding gene clusters formalized by nested common intervals between two genomes represented either as permutations or as sequences. Considering permutations, we give several algorithms whose running time depends on the size of the actual output rather than the output in the worst case. Indeed, we first provide a straightforward O(n 3) time algorithm for finding all nested common intervals. We reduce this complexity by providing an O(n 2) time algorithm computing an irredundant output. Finally, we show, by providing a third algorithm, that finding only the maximal nested common intervals can be done in linear time. Considering sequences, we provide solutions (modifications of previously defined algorithms and a new algorithm) for different variants of the problem, depending on the treatment one wants to apply to duplicated genes.


Gene Cluster Linear Time Time Algorithm Identity Permutation Consecutive Integer 
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 2009

Authors and Affiliations

  • Guillaume Blin
    • 1
  • Jens Stoye
    • 2
  1. 1.Université Paris-Est, LIGM - UMR CNRS 8049France
  2. 2.Technische FakultätUniversität BielefeldGermany

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