| | |
Summary: Longest subsequences in permutations
M. H. Albert
R. E. L. Aldred
M. D. Atkinson
H. P. van Ditmarsch
B. D. Handley
C. C. Handley
J. Opatrny
October 24, 2002
Abstract
For a class of permutations X the LXS problem is to identify in a given
permutation of length n its longest subsequence that is isomorphic to
a permutation of X. In general LXS is NP-hard. A general construction
that produces polynomial time algorithms for many classes X is given.
More efficient algorithms are given when X is defined by avoiding some
set of permutations of length 3.
Keywords pattern containment, permutations, longest subsequence
1 Introduction
The properties of the Longest Increasing Subsequence (LIS) of a sequence of
values have been studied for many years. In the case where the sequence of
|
