Parameterized approximation of dominating set problems

A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no k- Dominating Set, or (2) produces a dominating set of size at most g ( k ) , where g ( k ) is some fixed function of k. Such an outcome is termed an FPT appr...

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Bibliographic Details
Published in:Information processing letters Vol. 109; no. 1; pp. 68 - 70
Main Authors: Downey, Rodney G., Fellows, Michael R., McCartin, Catherine, Rosamond, Frances
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.12.2008
Elsevier
Elsevier Sequoia S.A
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Approximation
Approximation algorithms
Computer science; control theory; systems
Exact sciences and technology
FPT approximation
Information retrieval. Graph
Mathematical problems
Miscellaneous
Parameterized complexity
Studies
Theoretical computing
FPT approximation
Approximation algorithms
Parameterized complexity
Approximation
Dominating set
Computer theory
Information processing
Independent set
Approximation algorithm
Algorithm analysis
Graph algorithm
Complexity
ISSN:0020-0190, 1872-6119
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Summary:A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no k- Dominating Set, or (2) produces a dominating set of size at most g ( k ) , where g ( k ) is some fixed function of k. Such an outcome is termed an FPT approximation algorithm. We describe some results that begin to provide some answers. We show that there is no such FPT algorithm for g ( k ) of the form k + c (where c is a fixed constant, termed an additive FPT approximation), unless FPT = W [ 2 ] . We answer the analogous problem completely for the related Independent Dominating Set (IDS) problem, showing that IDS does not admit an FPT approximation algorithm, for any g ( k ) , unless FPT = W [ 2 ] .
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2008.09.017