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Erschienen in:
Preliminaries Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

5. More on Kernelization

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

Erschienen in: Fundamentals of Parameterized Complexity

Verlag: Springer London

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Abstract

We look at further kernelization techniques and in particular Turing kernels and kernelizations based upon Crown Structures.

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Vorheriges Kapitel Kernelization
Nächstes Kapitel Iterative Compression, and Measure and Conquer, for Minimization Problems
Fußnoten
1
If you are not familiar with this, read the material on Menger’s Theorems in Chap. 35.
 
2
Specifically, what is proven there is that if this problem has a polynomial size kernel then the polynomial-time hierarchy collapses to two or fewer levels.
 
3
As we saw in Chap. 1, in classical computability theory, and standard structural complexity theory, a many–one reduction is a (computable) (or polynomial) function \(f:L\to \widehat {L}\) such that x∈L iff \(f(x)\in \widehat {L}\). The “many” is that it is possible that for various x,y f(x)=f(y) as opposed to a 1–1 reduction where we insist that f is injective. If anything, the Fernau et al. reduction is really “one–many” since one question is being reduced to many. It is what is called a disjunctive truth table since it is the form x∈L iff \(\widehat {L}\) satisfies at least one of a polynomially computed (boolean) disjunction.
 
4
This kind of argument is carefully discussed in Chap. 34 when we look at e.g. Berge’s Criterion. If the reader is new to this kind of argument he or she should pause and read that part of Chap. 34 at this point.
 
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Metadaten
Titel
More on Kernelization
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_5