LIPIcs.FSTTCS.2009.2318.pdf
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Subexponential Algorithms for Partial Cover Problems
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2009-12-14
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Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, and Saket Saurabh. Subexponential Algorithms for Partial Cover Problems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 193-201, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2318
https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2318
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 $2^{\cO(k)}n^{\cO(1)}$.
Keywords
- Partial cover problems
- parameterized complexity
- subexponential time algorithms
- irrelevant vertex technique
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