A Complexity Dichotomy for Permutation Pattern Matching on Grid Classes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10415217" target="_blank" >RIV/00216208:11320/20:10415217 - isvavai.cz</a>

Výsledek na webu

<a href="https://drops.dagstuhl.de/opus/volltexte/2020/12718/" target="_blank" >https://drops.dagstuhl.de/opus/volltexte/2020/12718/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2020.52" target="_blank" >10.4230/LIPIcs.MFCS.2020.52</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Complexity Dichotomy for Permutation Pattern Matching on Grid Classes

Popis výsledku v původním jazyce

Permutation Pattern Matching (PPM) is the problem of deciding for a given pair of permutations π and τ whether the pattern π is contained in the text τ. Bose, Buss and Lubiw showed that PPM is NP-complete. In view of this result, it is natural to ask how the situation changes when we restrict the pattern π to a fixed permutation class ????; this is known as the ????-Pattern PPM problem. There have been several results in this direction, namely the work of Jelínek and Kynčl who completely resolved the hardness of ????-Pattern PPM when ???? is taken to be the class of σ-avoiding permutations for some σ. Grid classes are special kind of permutation classes, consisting of permutations admitting a grid-like decomposition into simpler building blocks. Of particular interest are the so-called monotone grid classes, in which each building block is a monotone sequence. Recently, it has been discovered that grid classes, especially the monotone ones, play a fundamental role in the understanding of the structure of general permutation classes. This motivates us to study the hardness of ????-Pattern PPM for a (monotone) grid class ????. We provide a complexity dichotomy for ????-Pattern PPM when ???? is taken to be a monotone grid class. Specifically, we show that the problem is polynomial-time solvable if a certain graph associated with ????, called the cell graph, is a forest, and it is NP-complete otherwise. We further generalize our results to grid classes whose blocks belong to classes of bounded grid-width. We show that the ????-Pattern PPM for such a grid class ???? is polynomial-time solvable if the cell graph of ???? avoids a cycle or a certain special type of path, and it is NP-complete otherwise.

Název v anglickém jazyce

A Complexity Dichotomy for Permutation Pattern Matching on Grid Classes

Popis výsledku anglicky

Permutation Pattern Matching (PPM) is the problem of deciding for a given pair of permutations π and τ whether the pattern π is contained in the text τ. Bose, Buss and Lubiw showed that PPM is NP-complete. In view of this result, it is natural to ask how the situation changes when we restrict the pattern π to a fixed permutation class ????; this is known as the ????-Pattern PPM problem. There have been several results in this direction, namely the work of Jelínek and Kynčl who completely resolved the hardness of ????-Pattern PPM when ???? is taken to be the class of σ-avoiding permutations for some σ. Grid classes are special kind of permutation classes, consisting of permutations admitting a grid-like decomposition into simpler building blocks. Of particular interest are the so-called monotone grid classes, in which each building block is a monotone sequence. Recently, it has been discovered that grid classes, especially the monotone ones, play a fundamental role in the understanding of the structure of general permutation classes. This motivates us to study the hardness of ????-Pattern PPM for a (monotone) grid class ????. We provide a complexity dichotomy for ????-Pattern PPM when ???? is taken to be a monotone grid class. Specifically, we show that the problem is polynomial-time solvable if a certain graph associated with ????, called the cell graph, is a forest, and it is NP-complete otherwise. We further generalize our results to grid classes whose blocks belong to classes of bounded grid-width. We show that the ????-Pattern PPM for such a grid class ???? is polynomial-time solvable if the cell graph of ???? avoids a cycle or a certain special type of path, and it is NP-complete otherwise.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA14-14179S" target="_blank" >GA14-14179S: Algoritmické, strukturální a složitostní aspekty konfigurací v rovině</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

ISBN

978-3-95977-159-7

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

18

Strana od-do

1-18

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Praha

Datum konání akce

24. 8. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—