Algorithms for Pattern Involvement in Permutations

  • Michael H. Albert
  • Robert E. L. Aldred
  • Mike D. Atkinson
  • Derek A. Holton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)


We consider the problem of developing algorithms for the recognition of a fixed pattern within a permutation. These methods are based upon using a carefully chosen chain or tree of subpatterns to build up the entire pattern. Generally, large improvements over brute force search can be obtained. Even using on-line versions of these methods allow for such improvements, though often not as great as for the full method. Furthermore, by using carefully chosen data structures to fine tune the methods, we establish that any pattern of length 4 can be detected in O(n log n) time. We also improve the complexity bound for detection of a separable pattern from O n 6 ) to O(n 5 log n).


Recognition Algorithm Pattern Involvement Permutation Graph Registration Information Brute Force Search 
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

  • Michael H. Albert
    • 1
  • Robert E. L. Aldred
    • 2
  • Mike D. Atkinson
    • 1
  • Derek A. Holton
    • 2
  1. 1.Department of Computer ScienceUniversity of OtagoOtagoNew Zealand
  2. 2.Department of Mathematics and StatisticsUniversity of OtagoOtagoNew Zealand

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