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Erschienen in:
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2013 | OriginalPaper | Buchkapitel

21. The Basic Class W[1] and an Analog of Cook’s Theorem

verfasst von : Rodney G. Downey, Michael R. Fellows

Erschienen in: Fundamentals of Parameterized Complexity

Verlag: Springer London

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Abstract

We introduce the basic class W[1] and prove the fundamental analogue of the Cook–Levin Theorem. This is central to much of the hardness theory for parameterized complexity.

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Vorheriges Kapitel Reductions
Nächstes Kapitel Some Other W[1] Hardness Results
Fußnoten
1
Of course, here we are using graphs for simplicity, but really this would be a τ-structure \(\mathcal{A}\) for some signature τ of the formulae φ. Graphs are universal anyway.
 
2
Note that the dual graph of a 2-interval graph is not necessarily a 2-interval graph so there is no contradiction from 1.
 
3
The definition of multiple interval graph in the previous exercise. For more hardness results for multiple interval graphs we refer the reader to Jiang [417] and Jiang and Zhang [418].
 
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Metadaten
Titel
The Basic Class W[1] and an Analog of Cook’s Theorem
verfasst von
Rodney G. Downey
Michael R. Fellows
Copyright-Jahr
2013
Verlag
Springer London
Buch
Fundamentals of Parameterized Complexity

Print ISBN: 978-1-4471-5558-4

Electronic ISBN: 978-1-4471-5559-1

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4471-5559-1_21