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### Subexponential Algorithms for Partial Cover Problems

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### Abstract

Partial Cover problems are optimization versions of fundamental and well studied problems like {\sc Vertex Cover} and {\sc Dominating Set}. Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number ($k$) of vertices, rather than covering all edges (or vertices). In general graphs, these problems are hard for parameterized complexity classes when parameterized by $k$. It was recently shown by Amini et. al. [{\em FSTTCS 08}\,] that {\sc Partial Vertex Cover} and {\sc Partial Dominating Set} are fixed parameter tractable on large classes of sparse graphs, namely $H$-minor free graphs, which include planar graphs and graphs of bounded genus. In particular, it was shown that on planar graphs both problems can be solved in time $2^{\cO(k)}n^{\cO(1)}$.

### BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2009:2318,
author =	{Fedor V. Fomin and Daniel Lokshtanov and Venkatesh Raman and Saket Saurabh},
title =	{{Subexponential  Algorithms for Partial Cover Problems}},
booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages =	{193--201},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-13-2},
ISSN =	{1868-8969},
year =	{2009},
volume =	{4},
editor =	{Ravi Kannan and K. Narayan Kumar},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},