Subexponential  Algorithms for Partial Cover Problems

Fomin, Fedor V.; Lokshtanov, Daniel; Raman, Venkatesh; Saurabh, Saket

doi:10.4230/LIPIcs.FSTTCS.2009.2318

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Subexponential Algorithms for Partial Cover Problems

Authors Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: 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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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2009.2318
URN: urn:nbn:de:0030-drops-23186

Subject Classification

Keywords

Partial cover problems
parameterized complexity
subexponential time algorithms
irrelevant vertex technique

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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 $2^{\cO(k)}n^{\cO(1)}$.

Cite As Get BibTex

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

Author Details

Fedor V. Fomin

Daniel Lokshtanov

Venkatesh Raman

Saket Saurabh

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