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Summary: Algorithms for pattern involvement in
permutations
M. H. Albert
Department of Computer Science
R. E. L. Aldred
Department of Mathematics and Statistics
M. D. Atkinson
Department of Computer Science
D. A. Holton
Department of Mathematics and Statistics
University of Otago
Abstract
We consider the problem of developing algorithms for the recognition
of a xed 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 provides such
improvements, though these are often not as great as for the full method.
Furthermore, by using carefully chosen data structures to ne tune the
methods, we establish that any pattern of length 4 can be detected in
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