Generalized Coloring of Permutations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10378317" target="_blank" >RIV/00216208:11320/18:10378317 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPIcs.ESA.2018.50" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ESA.2018.50</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ESA.2018.50" target="_blank" >10.4230/LIPIcs.ESA.2018.50</a>

Result language

angličtina

Original language name

Generalized Coloring of Permutations

Original language description

A permutation $pi$ is a emph{merge} of a permutation $sigma$ and a permutation $tau$, if we can color the elements of $pi$ red and blue so that the red elements have the same relative order as $sigma$ and the blue ones as~$tau$. We consider, for fixed hereditary permutation classes $cC$ and $cD$, the complexity of determining whether a given permutation $pi$ is a merge of an element of $cC$ with an element of~$cD$. We develop general algorithmic approaches for identifying polynomially tractable cases of merge recognition. Our tools include a version of nondeterministic logspace streaming recognizability of permutations, which we introduce, and a concept of bounded width decomposition, inspired by the work of Ahal and Rabinovich. As a consequence of the general results, we can provide nontrivial examples of tractable permutation merges involving commonly studied permutation classes, such as the class of layered permutations, the class of separable permutations, or the class of permutations avoiding a decreasing sequence of a given length. On the negative side, we obtain a general hardness result which implies, for example, that it is NP-complete to recognize the permutations that can be merged from two subpermutations avoiding the pattern 2413.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

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)

Publication year

2018

Confidentiality

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

Article name in the collection

26th Annual European Symposium on Algorithms (ESA 2018)

ISBN

978-3-95977-081-1

ISSN

1868-8969

e-ISSN

neuvedeno

Number of pages

14

Pages from-to

1-14

Publisher name

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Place of publication

Dagstuhl, Germany

Event location

Helsinky, Finsko

Event date

Aug 20, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

—