Solving Problems on Graphs of High Rank-Width

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Solving Problems on Graphs of High Rank-Width

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Solving Problems on Graphs of High Rank-Width

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Algorithmica

ISSN

0178-4617

e-ISSN

1432-0541

Svazek periodika

80

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

742-771

Kód UT WoS článku

000424203700014

EID výsledku v databázi Scopus

2-s2.0-85012292665