Towards a Polynomial Kernel for Directed Feedback Vertex Set

D 2017

Towards a Polynomial Kernel for Directed Feedback Vertex Set

EIBEN, Eduard, Sebastian ORDYNIAK, M.S. RAMANUJAN, Benjamin BERGOUGNOUX, Robert GANIAN et. al.

Základní údaje

Originální název

Towards a Polynomial Kernel for Directed Feedback Vertex Set

Autoři

EIBEN, Eduard (703 Slovensko), Sebastian ORDYNIAK (276 Německo), M.S. RAMANUJAN (356 Indie), Benjamin BERGOUGNOUX (250 Francie) a Robert GANIAN (203 Česká republika, garant, domácí)

Vydání

83. vyd. Nemecko, 42nd International Symposium on Mathematical Foundations of Computer Science, {MFCS} 2017, August 21-25, 2017 - Aalborg, Denmark, od s. 1-15, 15 s. 2017

Nakladatel

LIPIcs

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10200 1.2 Computer and information sciences

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

URL

Kód RIV

RIV/00216224:14330/17:00100550

Organizační jednotka

Fakulta informatiky

ISBN

978-3-95977-046-0

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.MFCS.2017.36

Klíčová slova anglicky

parameterized algorithms; kernelization; (directed) feedback vertex set

Štítky

core_A, firank_A

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 1. 2019 14:00, RNDr. Pavel Šmerk, Ph.D.

Anotace

V originále

In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph D and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every directed cycle of D. DFVS was shown to be fixed-parameter tractable when parameterized by solution size by Chen, Liu, Lu, O'Sullivan and Razgon [JACM 2008]; since then, the existence of a polynomial kernel for this problem has become one of the largest open problems in the area of parameterized algorithmics. In this paper, we study DFVS parameterized by the feedback vertex set number of the underlying undirected graph. We provide two main contributions: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus.

Citovat

EIBEN, Eduard, Sebastian ORDYNIAK, M.S. RAMANUJAN, Benjamin BERGOUGNOUX a Robert GANIAN. Towards a Polynomial Kernel for Directed Feedback Vertex Set. Online. In Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin. 42nd International Symposium on Mathematical Foundations of Computer Science, {MFCS} 2017, August 21-25, 2017 - Aalborg, Denmark. 83. vyd. Nemecko: LIPIcs, 2017, s. 1-15. ISBN 978-3-95977-046-0. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.MFCS.2017.36.

@inproceedings{1414043,
   author = {Eiben, Eduard and Ordyniak, Sebastian and Ramanujan, M.S. and Bergougnoux, Benjamin and Ganian, Robert},
   address = {Nemecko},
   booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science, {MFCS} 2017, August 21-25, 2017 - Aalborg, Denmark},
   doi = {http://dx.doi.org/10.4230/LIPIcs.MFCS.2017.36},
   edition = {83},
   editor = {Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
   keywords = {parameterized algorithms; kernelization; (directed) feedback vertex set},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Nemecko},
   isbn = {978-3-95977-046-0},
   pages = {1-15},
   publisher = {LIPIcs},
   title = {Towards a Polynomial Kernel for Directed Feedback Vertex Set},
   url = {http://drops.dagstuhl.de/opus/volltexte/2017/8112/},
   year = {2017}
}

TY  - JOUR
ID  - 1414043
AU  - Eiben, Eduard - Ordyniak, Sebastian - Ramanujan, M.S. - Bergougnoux, Benjamin - Ganian, Robert
PY  - 2017
TI  - Towards a Polynomial Kernel for Directed Feedback Vertex Set
PB  - LIPIcs
CY  - Nemecko
SN  - 9783959770460
KW  - parameterized algorithms
KW  - kernelization
KW  - (directed) feedback vertex set
UR  - http://drops.dagstuhl.de/opus/volltexte/2017/8112/
L2  - http://drops.dagstuhl.de/opus/volltexte/2017/8112/
N2  - In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph D and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every directed cycle of D. DFVS was shown to be fixed-parameter tractable when parameterized by solution size by Chen, Liu, Lu, O'Sullivan and Razgon [JACM 2008]; since then, the existence of a polynomial kernel for this problem has become one of the largest open problems in the area of parameterized algorithmics. In this paper, we study DFVS parameterized by the feedback vertex set number of the underlying undirected graph. We provide two main contributions: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus.
ER  -

EIBEN, Eduard, Sebastian ORDYNIAK, M.S. RAMANUJAN, Benjamin BERGOUGNOUX a Robert GANIAN. Towards a Polynomial Kernel for Directed Feedback Vertex Set. Online. In Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin. \textit{42nd International Symposium on Mathematical Foundations of Computer Science, $\{$MFCS$\}$ 2017, August 21-25, 2017 - Aalborg, Denmark}. 83. vyd. Nemecko: LIPIcs, 2017, s.~1-15. ISBN~978-3-95977-046-0. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.MFCS.2017.36.

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