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Author, Editor
Author(s):
Mnich, Matthias
Philip, Geevarghese
Saurabh, Saket
Suchy, Ondrej		dblp
dblp
dblp
dblp
Not MPG Author(s):
Saurabh, Saket
Suchy, Ondrej
Editor(s):
D'Souza, Deepak
Kavitha, Telikepalli
Radhakrishnan, Jaikumar		dblp
dblp
dblp
Not MPII Editor(s):
D'Souza, Deepak
Kavitha, Telikepalli
Radhakrishnan, Jaikumar

BibTeX cite key*:

MnichPhilipSaurabhSuchy2012a

Title, Conference

Title*:

Beyond Max-Cut: lambda-Extendible Properties
Parameterized Above the Poljak-Turzík Bound


published.pdf (594.22 KB)

Booktitle*:

32nd International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Event Address*:

Hyderabad, India
URL of the conference:

http://www.fsttcs.org

Event Date*:
(no longer used):


URL for downloading the paper:

http://drops.dagstuhl.de/opus/volltexte/2012/3877/

Event Start Date:

15 December 2012
Event End Date:

17 December 2012

Language:

English
Organization:

Indian Association for Research in Computing Science (IARCS)

Publisher

Publisher's Name:

Schloss Dagstuhl/ Leibniz-Zentrum für Informatik

Publisher's URL:

http://www.dagstuhl.de/

Address*:

Dagstuhl
Type:


Vol, No, pp., Year

Series:

Leibniz International Proceedings in Informatics

Volume:

18
Number:


Month:

December
Pages:

412-423



Sequence Number:


Year*:

2012
ISBN/ISSN:

978-3-939897-47-7


10.4230/LIPIcs.FSTTCS.2012.412


Abstract, Links, ©

URL for Reference:


Note:


(LaTeX) Abstract:

Poljak and Turz{\'{i}}k (Discrete Math.\ 1986) introduced the notion of $\lambda$-extendible
properties of graphs as a generalization of the property of
being bipartite. They showed that for any $0<\lambda<1$ and
$\lambda$-extendible property $\Pi$, any connected graph $G$ on $n$ vertices
and $m$ edges contains a spanning subgraph $H\in\Pi$ with at
least $\lambda{}m+\frac{1-\lambda}{2}(n-1)$ edges. The
property of being bipartite is $\lambda$-extendible for $\lambda=1/2$, and
thus the Poljak-Turz\'{i}k bound generalizes the well-known
Edwards-Erd\H{o}s bound for \textsc{Max-Cut}.

We define a variant, namely \emph{strong}
$\lambda$-extendibility, to which the Poljak-Turz\'{i}k bound applies. For a
strongly $\lambda$-extendible graph property $\Pi$, we define the parameterized
\textsc{Above Poljak-Turz\'{\i}k ($\Pi$)} problem as follows: Given a connected graph \(G\) on
$n$ vertices and $m$ edges and an integer parameter $k$, does
there exist a spanning subgraph $H$ of $G$ such that $H\in\Pi$
and $H$ has at least $\lambda{}m+\frac{1-\lambda}{2}(n-1)+k$
edges? The parameter is $k$, the surplus over the number of
edges guaranteed by the Poljak-Turz\'{i}k bound.

We consider properties $\Pi$ for which the \textsc{Above Poljak-Turz\'{\i}k ($\Pi$)} problem is
fixed-parameter tractable (FPT) on graphs which are $O(k)$
vertices away from being a graph in which each block is a
clique. We show that for all such properties, \textsc{Above Poljak-Turz\'{\i}k ($\Pi$)} is FPT
for all $0<\lambda<1$. Our results hold for properties of
oriented graphs and graphs with edge labels.

Our results generalize the recent result of Crowston et
al. (ICALP 2012) on \textsc{Max-Cut} parameterized above the
Edwards-Erd\H{o}s bound, and yield \textsf{FPT} algorithms for several graph
problems parameterized above lower bounds. For instance, we get
that the above-guarantee \textsc{Max $q$-Colorable Subgraph} problem is \textsf{FPT}. Our results
also imply that the parameterized above-guarantee \textsc{Oriented Max Acyclic Digraph}
problem
is \textsf{FPT}, thus solving an open question of Raman and Saurabh
(Theor.\ Comput.\ Sci.\ 2006).

URL for the Abstract:




Tags, Categories, Keywords:

Parameterized Algorithms, Above-Guarantee Parameterization, Max-Cut

HyperLinks / References / URLs:

http://drops.dagstuhl.de/opus/volltexte/2012/3877/

Copyright Message:


Personal Comments:


Download
Access Level:

Public

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:
@INPROCEEDINGS{MnichPhilipSaurabhSuchy2012a,
AUTHOR = {Mnich, Matthias and Philip, Geevarghese and Saurabh, Saket and Suchy, Ondrej},
 EDITOR = {D'Souza, Deepak and Kavitha, Telikepalli and Radhakrishnan, Jaikumar},
 TITLE = {Beyond Max-Cut: lambda-Extendible Properties
Parameterized Above the {Poljak-Turz{\'i}k} Bound},
 BOOKTITLE = {32nd International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
 PUBLISHER = {Schloss Dagstuhl/ Leibniz-Zentrum für Informatik},
 YEAR = {2012},
 ORGANIZATION = {Indian Association for Research in Computing Science (IARCS)},
 VOLUME = {18},
 PAGES = {412--423},
 SERIES = {Leibniz International Proceedings in Informatics},
 ADDRESS = {Hyderabad, India},
 MONTH = {December},
 ISBN = {978-3-939897-47-7},
 DOI = {10.4230/LIPIcs.FSTTCS.2012.412},
}

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Editor(s)
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Anja Becker
Anja Becker
Uwe Brahm
Geevarghese Philip
Geevarghese Philip		Edit Dates
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08.02.2013 12:02:33
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