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On the existence of subexponential parameterized algorithms

✍ Scribed by Liming Cai; David Juedes

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
249 KB
Volume
67
Category
Article
ISSN
0022-0000

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✦ Synopsis

The existence of subexponential-time parameterized algorithms is examined for various parameterized problems solvable in time Oð2 OðkÞ pðnÞÞ: It is shown that for each tX1; there are parameterized problems in FPT for which the existence of Oð2 oðkÞ pðnÞÞ-time parameterized algorithms implies the collapse of W ½t to FPT. Evidence is demonstrated that Max-SNP-hard optimization problems do not admit subexponentialtime parameterized algorithms. In particular, it is shown that each Max-SNP-complete problem is solvable in time Oð2 oðkÞ pðnÞÞ if and only if 3-SATADTIMEð2 oðnÞ Þ: These results are also applied to show evidence for the non-existence of Oð2 oð ffiffi k p Þ pðnÞÞ-time parameterized algorithms for a number of other important problems such as Dominating Set, Vertex Cover, and Independent Set on planar graph instances.

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