On Structural Parameterizations of the Bounded-Degree Vertex
Deletion Problem

D 2018

On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

GANIAN, Robert, Fabian KLUTE and Sebastian ORDYNIAK

Basic information

Original name

On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

Authors

GANIAN, Robert (203 Czech Republic, guarantor, belonging to the institution), Fabian KLUTE (276 Germany) and Sebastian ORDYNIAK (276 Germany)

Edition

Nemecko, STACS 2018, p. 1-14, 14 pp. 2018

Publisher

Dagstuhl

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

RIV identification code

RIV/00216224:14330/18:00106812

Organization unit

Faculty of Informatics

ISBN

978-3-95977-062-0

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.STACS.2018.33

UT WoS

000521090200033

Keywords in English

bounded-degree vertex deletion; feedback vertex set; parameterized algorithms; treecut width

Abstract

V originále

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. We thereby resolve the main open question stated in Betzler, Bredereck, Niedermeier and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex set number. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to the decompositional parameter treecut width and a novel problem-specific parameter called the core fracture number.

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

GANIAN, Robert, Fabian KLUTE and Sebastian ORDYNIAK. On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem. Online. In Rolf Niedermeier, Brigitte Vallee. STACS 2018. Nemecko: Dagstuhl, 2018, p. 1-14. ISBN 978-3-95977-062-0. Available from: https://dx.doi.org/10.4230/LIPIcs.STACS.2018.33.

@inproceedings{1523738,
   author = {Ganian, Robert and Klute, Fabian and Ordyniak, Sebastian},
   address = {Nemecko},
   booktitle = {STACS 2018},
   doi = {http://dx.doi.org/10.4230/LIPIcs.STACS.2018.33},
   editor = {Rolf Niedermeier, Brigitte Vallee},
   keywords = {bounded-degree vertex deletion; feedback vertex set; parameterized algorithms; treecut width},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Nemecko},
   isbn = {978-3-95977-062-0},
   pages = {1-14},
   publisher = {Dagstuhl},
   title = {On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem},
   year = {2018}
}

TY  - JOUR
ID  - 1523738
AU  - Ganian, Robert - Klute, Fabian - Ordyniak, Sebastian
PY  - 2018
TI  - On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem
PB  - Dagstuhl
CY  - Nemecko
SN  - 9783959770620
KW  - bounded-degree vertex deletion
KW  - feedback vertex set
KW  - parameterized algorithms
KW  - treecut width
N2  - We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. We thereby resolve the main open question stated in Betzler, Bredereck, Niedermeier and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex set number. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to the decompositional parameter treecut width and a novel problem-specific parameter called the core fracture number.
ER  -

GANIAN, Robert, Fabian KLUTE and Sebastian ORDYNIAK. On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem. Online. In Rolf Niedermeier, Brigitte Vallee. \textit{STACS 2018}. Nemecko: Dagstuhl, 2018, p.~1-14. ISBN~978-3-95977-062-0. Available from: https://dx.doi.org/10.4230/LIPIcs.STACS.2018.33.

Detailed Information on Publication Record