Griddings of Permutations and Hardness of Pattern Matching
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10431882" target="_blank" >RIV/00216208:11320/21:10431882 - isvavai.cz</a>
Result on the web
<a href="https://drops.dagstuhl.de/opus/volltexte/2021/14505/" target="_blank" >https://drops.dagstuhl.de/opus/volltexte/2021/14505/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.65" target="_blank" >10.4230/LIPIcs.MFCS.2021.65</a>
Alternative languages
Result language
angličtina
Original language name
Griddings of Permutations and Hardness of Pattern Matching
Original language description
We study the complexity of the decision problem known as Permutation Pattern Matching, or PPM. The input of PPM consists of a pair of permutations τ (the "text") and π (the "pattern"), and the goal is to decide whether τ contains π as a subpermutation. On general inputs, PPM is known to be NP-complete by a result of Bose, Buss and Lubiw. In this paper, we focus on restricted instances of PPM where the text is assumed to avoid a fixed (small) pattern σ; this restriction is known as Av(σ)-PPM. It has been previously shown that Av(σ)-PPM is polynomial for any σ of size at most 3, while it is NP-hard for any σ containing a monotone subsequence of length four. In this paper, we present a new hardness reduction which allows us to show, in a uniform way, that Av(σ)-PPM is hard for every σ of size at least 6, for every σ of size 5 except the symmetry class of 41352, as well as for every σ symmetric to one of the three permutations 4321, 4312 and 4231. Moreover, assuming the exponential time hypothesis, none of these hard cases of Av(σ)-PPM can be solved in time 2^o(n/log n). Previously, such conditional lower bound was not known even for the unconstrained PPM problem. On the tractability side, we combine the CSP approach of Guillemot and Marx with the structural results of Huczynska and Vatter to show that for any monotone-griddable permutation class ????, PPM is polynomial when the text is restricted to a permutation from ????.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA18-19158S" target="_blank" >GA18-19158S: Algorithmic, structural and complexity aspects of geometric and other configurations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
ISBN
978-3-95977-201-3
ISSN
1868-8969
e-ISSN
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Number of pages
22
Pages from-to
1-22
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum für Informatik
Place of publication
Dagstuhl, Germany
Event location
Tallinn, Estonsko
Event date
Aug 23, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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