Meta-kernelization using well-structured modulators

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00106819" target="_blank" >RIV/00216224:14330/18:00106819 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.dam.2017.09.018" target="_blank" >http://dx.doi.org/10.1016/j.dam.2017.09.018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.dam.2017.09.018" target="_blank" >10.1016/j.dam.2017.09.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Meta-kernelization using well-structured modulators

Popis výsledku v původním jazyce

Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been successfully used to obtain polynomial kernels for a wide range of problems. Many of these parameters can be defined as the size of a smallest modulator of the given graph into a fixed graph class (i.e., a set of vertices whose deletion puts the graph into the graph class). Such parameters admit the construction of polynomial kernels even when the solution size is large or not applicable. This work follows up on the research on meta-kernelization frameworks in terms of structural parameters. We develop a class of parameters which are based on a more general view on modulators: instead of size, the parameters employ a combination of rank-width and split decompositions to measure structure inside the modulator. This allows us to lift kernelization results from modulator-size to more general parameters, hence providing small kernels even in cases where previously developed approaches could not be applied. We show (i) how such large but well-structured modulators can be efficiently approximated, (ii) how they can be used to obtain polynomial kernels for graph problems expressible in Monadic Second Order logic, and (iii) how they support the extension of previous results in the area of structural meta-kernelization.

Název v anglickém jazyce

Meta-kernelization using well-structured modulators

Popis výsledku anglicky

Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been successfully used to obtain polynomial kernels for a wide range of problems. Many of these parameters can be defined as the size of a smallest modulator of the given graph into a fixed graph class (i.e., a set of vertices whose deletion puts the graph into the graph class). Such parameters admit the construction of polynomial kernels even when the solution size is large or not applicable. This work follows up on the research on meta-kernelization frameworks in terms of structural parameters. We develop a class of parameters which are based on a more general view on modulators: instead of size, the parameters employ a combination of rank-width and split decompositions to measure structure inside the modulator. This allows us to lift kernelization results from modulator-size to more general parameters, hence providing small kernels even in cases where previously developed approaches could not be applied. We show (i) how such large but well-structured modulators can be efficiently approximated, (ii) how they can be used to obtain polynomial kernels for graph problems expressible in Monadic Second Order logic, and (iii) how they support the extension of previous results in the area of structural meta-kernelization.

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

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

—

Svazek periodika

248

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

153-167

Kód UT WoS článku

000447109400015

EID výsledku v databázi Scopus

2-s2.0-85033494153