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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| Published in: | Information processing letters Vol. 109; no. 1; pp. 68 - 70 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
16.12.2008
Elsevier Elsevier Sequoia S.A |
| Subjects: | |
| ISSN: | 0020-0190, 1872-6119 |
| Online Access: | Get full text |
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| Abstract | 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
]
. |
|---|---|
| AbstractList | 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]. [PUBLICATION ABSTRACT] 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 ] . |
| Author | McCartin, Catherine Downey, Rodney G. Rosamond, Frances Fellows, Michael R. |
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| Cites_doi | 10.1093/comjnl/bxm048 10.1137/S0097539703427203 10.1016/j.orl.2007.02.008 |
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| Keywords | FPT approximation Approximation algorithms Parameterized complexity Approximation Dominating set Computer theory Information processing Independent set Approximation algorithm Algorithm analysis Graph algorithm Complexity |
| Language | English |
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| References | Downey, McCartin (bib004) 2004; vol. 3162 Chen, Grohe, Grüber (bib001) 2006; vol. 4169 Cai, Huang (bib002) 2006; vol. 4169 C.M. McCartin, P. Rossmanith, M. Fellows, Frontiers of intractability for dominating set, Manuscript, 2007 Niedermeier (bib011) 2006 Flum, Grohe (bib005) 2004; 33 Grohe, Grüber (bib006) 2007; vol. 4596 Downey, Fellows (bib003) 1999 Marx (bib008) 2008; 36 C.M. McCartin, Contributions to parameterized complexity, PhD thesis, Victoria University, Wellington, 2003 Marx (bib007) 2008; 51 Downey (10.1016/j.ipl.2008.09.017_bib003) 1999 Grohe (10.1016/j.ipl.2008.09.017_bib006) 2007; vol. 4596 Marx (10.1016/j.ipl.2008.09.017_bib008) 2008; 36 10.1016/j.ipl.2008.09.017_bib010 Marx (10.1016/j.ipl.2008.09.017_bib007) 2008; 51 Flum (10.1016/j.ipl.2008.09.017_bib005) 2004; 33 Niedermeier (10.1016/j.ipl.2008.09.017_bib011) 2006 Chen (10.1016/j.ipl.2008.09.017_bib001) 2006; vol. 4169 10.1016/j.ipl.2008.09.017_bib009 Cai (10.1016/j.ipl.2008.09.017_bib002) 2006; vol. 4169 Downey (10.1016/j.ipl.2008.09.017_bib004) 2004; vol. 3162 |
| References_xml | – volume: vol. 4169 start-page: 109 year: 2006 end-page: 120 ident: bib001 article-title: On parameterized approximability publication-title: Proceedings of the Second International Workshop on Parameterized and Exact Computation – reference: C.M. McCartin, P. Rossmanith, M. Fellows, Frontiers of intractability for dominating set, Manuscript, 2007 – year: 2006 ident: bib011 article-title: Invitation to Fixed-Parameter Algorithms – volume: vol. 4596 start-page: 363 year: 2007 end-page: 374 ident: bib006 article-title: Parameterized approximability of the disjoint cycle problem publication-title: Proceedings of ICALP 2007 – volume: 33 start-page: 892 year: 2004 end-page: 922 ident: bib005 article-title: The parameterized complexity of counting problems publication-title: SIAM Journal on Computing – volume: vol. 4169 start-page: 96 year: 2006 end-page: 108 ident: bib002 article-title: Fixed parameter approximation: Conceptual framework and approximability results publication-title: Proceedings of the Second International Workshop on Parameterized and Exact Computation – year: 1999 ident: bib003 article-title: Parameterized Complexity – volume: vol. 3162 start-page: 13 year: 2004 end-page: 24 ident: bib004 article-title: Online problems, pathwidth, and persistence publication-title: Proceedings of IWPEC 2004 – volume: 51 start-page: 60 year: 2008 end-page: 78 ident: bib007 article-title: Parameterized complexity and approximation algorithms publication-title: The Computer Journal – volume: 36 start-page: 31 year: 2008 end-page: 36 ident: bib008 article-title: Searching the publication-title: Operations Research Letters – reference: C.M. McCartin, Contributions to parameterized complexity, PhD thesis, Victoria University, Wellington, 2003 – volume: vol. 4169 start-page: 96 year: 2006 ident: 10.1016/j.ipl.2008.09.017_bib002 article-title: Fixed parameter approximation: Conceptual framework and approximability results – volume: 51 start-page: 60 issue: 1 year: 2008 ident: 10.1016/j.ipl.2008.09.017_bib007 article-title: Parameterized complexity and approximation algorithms publication-title: The Computer Journal doi: 10.1093/comjnl/bxm048 – year: 2006 ident: 10.1016/j.ipl.2008.09.017_bib011 – year: 1999 ident: 10.1016/j.ipl.2008.09.017_bib003 – ident: 10.1016/j.ipl.2008.09.017_bib009 – ident: 10.1016/j.ipl.2008.09.017_bib010 – volume: vol. 4169 start-page: 109 year: 2006 ident: 10.1016/j.ipl.2008.09.017_bib001 article-title: On parameterized approximability – volume: 33 start-page: 892 issue: 4 year: 2004 ident: 10.1016/j.ipl.2008.09.017_bib005 article-title: The parameterized complexity of counting problems publication-title: SIAM Journal on Computing doi: 10.1137/S0097539703427203 – volume: vol. 3162 start-page: 13 year: 2004 ident: 10.1016/j.ipl.2008.09.017_bib004 article-title: Online problems, pathwidth, and persistence – volume: 36 start-page: 31 issue: 1 year: 2008 ident: 10.1016/j.ipl.2008.09.017_bib008 article-title: Searching the k-change neighborhood for TSP is W[1]-hard publication-title: Operations Research Letters doi: 10.1016/j.orl.2007.02.008 – volume: vol. 4596 start-page: 363 year: 2007 ident: 10.1016/j.ipl.2008.09.017_bib006 article-title: Parameterized approximability of the disjoint cycle problem |
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| Snippet | 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... 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,... |
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| StartPage | 68 |
| SubjectTerms | 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 |
| Title | Parameterized approximation of dominating set problems |
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