Permutation Pattern matching in (213, 231)-avoiding permutations

Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where...

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Vydané v:Discrete mathematics and theoretical computer science Ročník 18 no. 2, Permutation...; číslo Permutation Patterns; s. 14.1 - 22
Hlavní autori: Neou, Both, Rizzi, Romeo, Vialette, Stéphane
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: DMTCS 22.03.2017
Discrete Mathematics & Theoretical Computer Science
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[info.info-bi] computer science [cs]/bioinformatics [q-bio.qm]
[info.info-cc] computer science [cs]/computational complexity [cs.cc]
avoiding permutation
Bioinformatics
Computational Complexity
Computer Science
pattern avoidance
pattern matching
permutation class
permutation pattern
Permutation Pattern
Pattern Matching
Permutation Class
Pattern Avoidance
avoiding permutation
ISSN:1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí:Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where only σ avoids 213 and 231, we present a O(max(kn 2 , n 2 log log n)-time algorithm. We extend our research to bivincular patterns that avoid 213 and 231 and present a O(kn 4)-time algorithm. Finally we look at the related problem of the longest subsequence which avoids 213 and 231.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.1329