Meta-kernelization using well-structured modulators

J 2018

Meta-kernelization using well-structured modulators

EIBEN, Eduard, Robert GANIAN and Stefan SZEIDER

Basic information

Original name

Meta-kernelization using well-structured modulators

Authors

EIBEN, Eduard (703 Slovakia), Robert GANIAN (203 Czech Republic, guarantor, belonging to the institution) and Stefan SZEIDER (40 Austria)

Edition

Discrete Applied Mathematics, Elsevier Science, 2018, 0166-218X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 0.983

RIV identification code

RIV/00216224:14330/18:00106819

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1016/j.dam.2017.09.018

UT WoS

000447109400015

Keywords in English

kernelization; modulators; parameterized complexity

Abstract

V originále

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.

Links

MSM0021622419, plan (intention)

Name: Vysoce paralelní a distribuované výpočetní systémy

Investor: Ministry of Education, Youth and Sports of the CR, Highly Parallel and Distributed Computing Systems

Citovat

EIBEN, Eduard, Robert GANIAN and Stefan SZEIDER. Meta-kernelization using well-structured modulators. Discrete Applied Mathematics. Elsevier Science, 2018, vol. 248, No 1, p. 153-167. ISSN 0166-218X. Available from: https://dx.doi.org/10.1016/j.dam.2017.09.018.

@article{1523840,
   author = {Eiben, Eduard and Ganian, Robert and Szeider, Stefan},
   article_number = {1},
   doi = {http://dx.doi.org/10.1016/j.dam.2017.09.018},
   keywords = {kernelization; modulators; parameterized complexity},
   language = {eng},
   issn = {0166-218X},
   journal = {Discrete Applied Mathematics},
   title = {Meta-kernelization using well-structured modulators},
   volume = {248},
   year = {2018}
}

TY  - JOUR
ID  - 1523840
AU  - Eiben, Eduard - Ganian, Robert - Szeider, Stefan
PY  - 2018
TI  - Meta-kernelization using well-structured modulators
JF  - Discrete Applied Mathematics
VL  - 248
IS  - 1
SP  - 153-167
EP  - 153-167
PB  - Elsevier Science
SN  - 0166218X
KW  - kernelization
KW  - modulators
KW  - parameterized complexity
N2  - 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.
ER  -

EIBEN, Eduard, Robert GANIAN and Stefan SZEIDER. Meta-kernelization using well-structured modulators. \textit{Discrete Applied Mathematics}. Elsevier Science, 2018, vol.~248, No~1, p.~153-167. ISSN~0166-218X. Available from: https://dx.doi.org/10.1016/j.dam.2017.09.018.

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