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@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Ambalath, Abhimanyu M.
Balasundaram, Radheshyam
H., Chintan Rao
Koppula, Venkata
Misra, Neeldhara
Philip, Geevarghese
Ramanujan, M. S.
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Not MPG Author(s):
Ambalath, Abhimanyu M.
Balasundaram, Radheshyam
H., Chintan Rao
Koppula, Venkata
Misra, Neeldhara
Ramanujan, M. S.
Editor(s):
Raman, Venkatesh
Saurabh, Saket
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dblp
Not MPII Editor(s):
Raman, Venkatesh
Saurabh, Saket
BibTeX cite key*:
AmbalathBalasundaramHKoppulaMisraPhilipRamanujan2010
Title, Booktitle
Title*:
On the Kernelization Complexity of Colorful Motifs
cm-ipec.pdf (329.64 KB)
Booktitle*:
Parameterized and Exact Computation - 5th International Symposium, IPEC 2010, Chennai, India, December 13-15, 2010. Proceedings
Event, URLs
Conference URL::
http://www.imsc.res.in/ipec/
Downloading URL:
http://www.springerlink.com/content/cx67550631830076/fulltext.pdf
Event Address*:
Chennai, India
Language:
English
Event Date*
(no longer used):
Organization:
Event Start Date:
13 December 2010
Event End Date:
15 December 2010
Publisher
Name*:
Springer
URL:
http://www.springer.com
Address*:
Berlin
Type:
Vol, No, Year, pp.
Series:
Lecture Notes in Computer Science
Volume:
6478
Number:
Month:
Pages:
14-25
Year*:
2010
VG Wort Pages:
ISBN/ISSN:
978-3-642-17492-6
Sequence Number:
DOI:
10.1007/978-3-642-17493-3
Note, Abstract, ©
(LaTeX) Abstract:
The {\sc Colorful Motif} problem asks if, given a vertex-colored
graph $G$, there exists a subset $S$ of vertices of $G$ such
that the graph induced by $G$ on $S$ is connected and contains
every color in the graph exactly once. The problem is motivated
by applications in computational biology and is also
well-studied from the theoretical point of view. In particular,
it is known to be NP-complete even on trees of maximum degree
three~[Fellows et al, ICALP 2007]. In their pioneering paper
that introduced the color-coding technique, Alon et al.~[STOC
1995] show, {\em inter alia}, that the problem is FPT on general
graphs. More recently, Cygan et al.~[WG 2010] showed that {\sc
Colorful Motif} is NP-complete on {\em comb graphs}, a special
subclass of the set of trees of maximum degree three. They also
showed that the problem is not likely to admit polynomial
kernels on forests.

We continue the study of the kernelization
complexity of the {\sc Colorful Motif} problem restricted to
simple graph classes. Surprisingly, the infeasibility of
polynomial kernelization persists even when the input is
restricted to comb graphs. We demonstrate this by showing a
simple but novel composition algorithm. Further, we show that
the problem restricted to comb graphs admits polynomially many
polynomial kernels. To our knowledge, there are very few
examples of problems with many polynomial kernels known in the
literature. We also show hardness of polynomial kernelization
for certain variants of the problem on trees; this rules out a
general class of approaches for showing many polynomial kernels
for the problem restricted to trees. Finally, we show that the
problem is unlikely to admit polynomial kernels on another
simple graph class, namely the set of all graphs of diameter
two. As an application of our results, we settle the classical complexity of \cds{} on graphs of diameter two --- specifically, we show that it is \NPC.
URL for the Abstract:
http://www.springerlink.com/content/cx67550631830076/
Keywords:
Parameterized Algorithms, Kernel lower bounds, Colorful Motif, Comb graphs
Copyright Message:
Copyright Springer-Verlag Berlin Heidelberg 2010. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,
in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law.

Published in the Proceedings of IPEC 2010, Chennai, India, December 13-15, 2010. Lecture Notes in Computer Science, Volume 6478. The original publication is available at www.springerlink.com : http://www.springerlink.com/content/cx67550631830076/
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{AmbalathBalasundaramHKoppulaMisraPhilipRamanujan2010,
AUTHOR = {Ambalath, Abhimanyu M. and Balasundaram, Radheshyam and H., Chintan Rao and Koppula, Venkata and Misra, Neeldhara and Philip, Geevarghese and Ramanujan, M. S.},
EDITOR = {Raman, Venkatesh and Saurabh, Saket},
TITLE = {On the Kernelization Complexity of Colorful Motifs},
BOOKTITLE = {Parameterized and Exact Computation - 5th International Symposium, IPEC 2010, Chennai, India, December 13-15, 2010. Proceedings},
PUBLISHER = {Springer},
YEAR = {2010},
VOLUME = {6478},
PAGES = {14--25},
SERIES = {Lecture Notes in Computer Science},
ADDRESS = {Chennai, India},
ISBN = {978-3-642-17492-6},
DOI = {10.1007/978-3-642-17493-3},
}


Entry last modified by Geevarghese Philip, 07/08/2014
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Editor
Geevarghese Philip
Geevarghese Philip


Edit Date
04/21/2012 06:44:30 PM
04/21/2012 05:31:36 PM



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