# Finding small patterns in permutations in linear time

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

Text
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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.

Item Type: | Book Section |
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Additional Information: | A4 ACM Special Interest Group on Algorithms; and Computation Theory (SIGACT); SIAM Activity Group on Discrete Mathematics |

Uncontrolled Keywords: | Clustering algorithms; Permutation patterns; Parameterized; Linear-time algorithms; Linear time |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 26 Sep 2014 19:16 |

Last Modified: | 26 Sep 2014 19:16 |

URI: | https://eprints.sztaki.hu/id/eprint/8001 |

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