Solving Problems on Graphs of High Rank-Width

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00106821" target="_blank" >RIV/00216224:14330/18:00106821 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s00453-017-0290-8" target="_blank" >http://dx.doi.org/10.1007/s00453-017-0290-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-017-0290-8" target="_blank" >10.1007/s00453-017-0290-8</a>

Result language

angličtina

Original language name

Solving Problems on Graphs of High Rank-Width

Original language description

A modulator in a graph is a vertex set whose deletion places the considered graph into some specified graph class. The cardinality of a modulator to various graph classes has long been used as a structural parameter which can be exploited to obtain fixed-parameter algorithms for a range of hard problems. Here we investigate what happens when a graph contains a modulator which is large but “well-structured” (in the sense of having bounded rank-width). Can such modulators still be exploited to obtain efficient algorithms? And is it even possible to find such modulators efficiently? We first show that the parameters derived from such well-structured modulators are more powerful for fixed-parameter algorithms than the cardinality of modulators and rank-width itself. Then, we develop a fixed-parameter algorithm for finding such well-structured modulators to every graph class which can be characterized by a finite set of forbidden induced subgraphs. We proceed by showing how well-structured modulators can be used to obtain efficient parameterized algorithms for Minimum Vertex Cover and Maximum Clique. Finally, we use the concept of well-structured modulators to develop an algorithmic meta-theorem for deciding problems expressible in monadic second order logic, and prove that this result is tight in the sense that it cannot be generalized to LinEMSO problems.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

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)

Project

—

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

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

Name of the periodical

Algorithmica

ISSN

0178-4617

e-ISSN

1432-0541

Volume of the periodical

80

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

30

Pages from-to

742-771

UT code for WoS article

000424203700014

EID of the result in the Scopus database

2-s2.0-85012292665