Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop


Show entries of:

this year (2019) | last year (2018) | two years ago (2017) | Notes URL

Action:

login to update

Options:




Library Locked Library locked




Author, Editor

Author(s):

Misra, Neeldhara
Philip, Geevarghese
Raman, Venkatesh
Saurabh, Saket

dblp
dblp
dblp
dblp

Not MPG Author(s):

Misra, Neeldhara
Raman, Venkatesh
Saurabh, Saket

Editor(s):

Lodaya, Kamal
Mahajan, Meena

dblp
dblp

Not MPII Editor(s):

Lodaya, Kamal
Mahajan, Meena

BibTeX cite key*:

MisraPhilipRamanSaurabh2010

Title, Booktitle

Title*:

The effect of girth on the kernelization complexity of Connected Dominating Set


girthcds.pdf (539.35 KB)

Booktitle*:

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, December 15-18, 2010, Chennai, India

Event, URLs

URL of the conference:

http://www.fsttcs.org/archives/2010/

URL for downloading the paper:

http://drops.dagstuhl.de/opus/volltexte/2010/2856/pdf/10.pdf

Event Address*:

Chennai, India

Language:

English

Event Date*
(no longer used):


Organization:


Event Start Date:

15 December 2010

Event End Date:

18 December 2010

Publisher

Name*:

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

URL:

http://www.dagstuhl.de/

Address*:

Dagstuhl, Germany

Type:


Vol, No, Year, pp.

Series:

Leibniz International Proceedings in Informatics

Volume:

8

Number:


Month:


Pages:

96-107

Year*:

2010

VG Wort Pages:


ISBN/ISSN:

978-3-939897-23-1

Sequence Number:


DOI:

10.4230/LIPIcs.FSTTCS.2010.96



Note, Abstract, ©


(LaTeX) Abstract:

In the Connected Dominating Set problem we are given as input a graph $G$ and a
positive integer $k$, and are asked if there is a set $S$ of at
most $k$ vertices of $G$ such that $S$ is a dominating set of
$G$ and the subgraph induced by $S$ is connected. This is a
basic connectivity problem that is known to be NP-complete, and it
has been extensively studied using several algorithmic
approaches. In this paper we study the effect of excluding short
cycles, as a subgraph, on the {\em kernelization complexity} of
Connected Dominating Set.

Kernelization algorithms are polynomial-time algorithms that
take an input and a positive integer $k$ (the {\em parameter})
and output an equivalent instance where the size of the new
instance and the new parameter are both bounded by some function
$g(k)$. The new instance is called a $g(k)$ {\em kernel} for
the problem. If $g(k)$ is a polynomial in $k$ then we say that
the problem admits polynomial kernels. The girth of a graph $G$
is the length of a shortest cycle in $G$. It turns out that
Connected Dominating Set is ``hard'' on graphs with small cycles, and becomes
progressively easier as the girth increases. More specifically,
we obtain the following interesting trichotomy: Connected Dominating Set

\begin{itemize}
\item does not have a kernel of {\em any} size on graphs of girth
$3$ or $4$ (since the problem is W[2]-hard);
\item admits a $g(k)$ kernel, where $g(k)$ is $k^{O(k)}$, on
graphs of girth $5$ or $6$ but has {\em no} polynomial kernel
(unless the Polynomial Hierarchy (PH) collapses to the third
level) on these graphs;
\item has a cubic ($O(k^3)$) kernel on graphs of girth at least $7$.
\end{itemize}
While there is a large and growing collection of parameterized
complexity results available for problems on graph classes
characterized by excluded {\em minors}, our results add to the
very few known in the field for graph classes characterized by
excluded {\em subgraphs}.

URL for the Abstract:

http://drops.dagstuhl.de/opus/volltexte/2010/2856/

Keywords:

Connected Dominating Set, Parameterized Complexity, Kernelization, Girth



Download
Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

Audience:

experts only

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort



BibTeX Entry:

@INPROCEEDINGS{MisraPhilipRamanSaurabh2010,
AUTHOR = {Misra, Neeldhara and Philip, Geevarghese and Raman, Venkatesh and Saurabh, Saket},
EDITOR = {Lodaya, Kamal and Mahajan, Meena},
TITLE = {The effect of girth on the kernelization complexity of Connected Dominating Set},
BOOKTITLE = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, December 15-18, 2010, Chennai, India},
PUBLISHER = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
YEAR = {2010},
VOLUME = {8},
PAGES = {96--107},
SERIES = {Leibniz International Proceedings in Informatics},
ADDRESS = {Chennai, India},
ISBN = {978-3-939897-23-1},
DOI = {10.4230/LIPIcs.FSTTCS.2010.96},
}


Entry last modified by Geevarghese Philip, 07/08/2014
Show details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)
Hide details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)

Editor(s)
[Library]
Created
04/21/2012 05:48:43 PM
Revision
1.
0.


Editor
Geevarghese Philip
Geevarghese Philip


Edit Date
12/08/2012 04:43:30 AM
04/21/2012 05:48:43 PM


Show details for Attachment SectionAttachment Section
Hide details for Attachment SectionAttachment Section

View attachments here:


File Attachment Icon
girthcds.pdf