Kernelization using structural parameters on sparse graph
classes

J 2017

Kernelization using structural parameters on sparse graph classes

GAJARSKÝ, Jakub, Petr HLINĚNÝ, Jan OBDRŽÁLEK, Sebastian ORDYNIAK, Felix REIDL et. al.

Basic information

Original name

Kernelization using structural parameters on sparse graph classes

Authors

GAJARSKÝ, Jakub (703 Slovakia, belonging to the institution), Petr HLINĚNÝ (203 Czech Republic, guarantor, belonging to the institution), Jan OBDRŽÁLEK (203 Czech Republic, belonging to the institution), Sebastian ORDYNIAK (276 Germany, belonging to the institution), Felix REIDL (276 Germany), Peter ROSSMANITH (276 Germany), Fernando VILLAAMIL (276 Germany) and Somnath SIKDAR (356 India)

Edition

Journal of Computer and System Sciences, SAN DIEGO, Elsevier, 2017, 0022-0000

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: 1.497

RIV identification code

RIV/00216224:14330/17:00094632

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1016/j.jcss.2016.09.002

UT WoS

000388430000015

Keywords in English

Parameterized complexity; Kernelization; Nowhere dense graphs; Finite integer index; Treedepth

Abstract

V originále

We prove that graph problems with finite integer index have linear kernels on graphs of bounded expansion when parameterized by the size of a modulator to constant-treedepth graphs. For nowhere dense graph classes, our result yields almost-linear kernels. We also argue that such a linear kernelization result with a weaker parameter would fail to include some of the problems covered by our framework. We only require the problems to have FII on graphs of constant treedepth. This allows to prove linear kernels also for problems such as Longest-Path/Cycle, Exact-s, t-Path, Treewidth, and Pathwidth, which do not have FII on general graphs. (C) 2016 Elsevier Inc. All rights reserved.

Links

GA14-03501S, research and development project

Name: Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky

Investor: Czech Science Foundation

MUNI/A/0945/2015, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace V.

Investor: Masaryk University, Category A

Citovat

GAJARSKÝ, Jakub, Petr HLINĚNÝ, Jan OBDRŽÁLEK, Sebastian ORDYNIAK, Felix REIDL, Peter ROSSMANITH, Fernando VILLAAMIL and Somnath SIKDAR. Kernelization using structural parameters on sparse graph classes. Journal of Computer and System Sciences. SAN DIEGO: Elsevier, 2017, vol. 84, No 1, p. 219-242. ISSN 0022-0000. Available from: https://dx.doi.org/10.1016/j.jcss.2016.09.002.

@article{1372352,
   author = {Gajarský, Jakub and Hliněný, Petr and Obdržálek, Jan and Ordyniak, Sebastian and Reidl, Felix and Rossmanith, Peter and Villaamil, Fernando and Sikdar, Somnath},
   article_location = {SAN DIEGO},
   article_number = {1},
   doi = {http://dx.doi.org/10.1016/j.jcss.2016.09.002},
   keywords = {Parameterized complexity; Kernelization; Nowhere dense graphs; Finite integer index; Treedepth},
   language = {eng},
   issn = {0022-0000},
   journal = {Journal of Computer and System Sciences},
   title = {Kernelization using structural parameters on sparse graph classes},
   volume = {84},
   year = {2017}
}

TY  - JOUR
ID  - 1372352
AU  - Gajarský, Jakub - Hliněný, Petr - Obdržálek, Jan - Ordyniak, Sebastian - Reidl, Felix - Rossmanith, Peter - Villaamil, Fernando - Sikdar, Somnath
PY  - 2017
TI  - Kernelization using structural parameters on sparse graph classes
JF  - Journal of Computer and System Sciences
VL  - 84
IS  - 1
SP  - 219-242
EP  - 219-242
PB  - Elsevier
SN  - 00220000
KW  - Parameterized complexity
KW  - Kernelization
KW  - Nowhere dense graphs
KW  - Finite integer index
KW  - Treedepth
N2  - We prove that graph problems with finite integer index have linear kernels on graphs of bounded expansion when parameterized by the size of a modulator to constant-treedepth graphs. For nowhere dense graph classes, our result yields almost-linear kernels. We also argue that such a linear kernelization result with a weaker parameter would fail to include some of the problems covered by our framework. We only require the problems to have FII on graphs of constant treedepth. This allows to prove linear kernels also for problems such as Longest-Path/Cycle, Exact-s, t-Path, Treewidth, and Pathwidth, which do not have FII on general graphs. (C) 2016 Elsevier Inc. All rights reserved.
ER  -

GAJARSKÝ, Jakub, Petr HLINĚNÝ, Jan OBDRŽÁLEK, Sebastian ORDYNIAK, Felix REIDL, Peter ROSSMANITH, Fernando VILLAAMIL and Somnath SIKDAR. Kernelization using structural parameters on sparse graph classes. \textit{Journal of Computer and System Sciences}. SAN DIEGO: Elsevier, 2017, vol.~84, No~1, p.~219-242. ISSN~0022-0000. Available from: https://dx.doi.org/10.1016/j.jcss.2016.09.002.

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