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 Author, Editor
 Author(s): Ambalath, Abhimanyu M. Balasundaram, Radheshyam H., Chintan Rao Koppula, Venkata Misra, Neeldhara Philip, Geevarghese Ramanujan, M. S. dblp dblp dblp dblp dblp dblp dblp 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 dblp 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
 URL of the conference: http://www.imsc.res.in/ipec/ URL for downloading the paper: 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

 (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},