Guillemot, Sylvain and Marx, Dániel (2014) Finding small patterns in permutations in linear time. In: 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms . Association for Computing Machinery, New York, pp. 82-101. ISBN 9781611973389

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Abstract

Given two permutations σ and π, the Permutation Pattern problem asks if a is σ subpattern of π. We show that the problem can be solved in time 2O(l2logl), n, where l = \ σ \ and n = | π |. In other words, the problem is fixed-parameter tractable parameterized by the size of the subpattern to be found. We introduce a novel type of decompositions for permutations and a corresponding width measure. We present a linear-time algorithm that either finds a as a subpattern of π, or finds a decomposition of π whose width is bounded by a function of \ σ \. Then we show how to solve the Permutation Pattern problem in linear time if a bounded-width decomposition is given in the input. Copyright © 2014 by the Society for Industrial and Applied Mathematics.

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