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Invitation to Fixed-Parameter Algorithms$
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Rolf Niedermeier

Print publication date: 2006

Print ISBN-13: 9780198566076

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566076.001.0001

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DATA REDUCTION AND PROBLEM KERNELS

DATA REDUCTION AND PROBLEM KERNELS

Chapter:
(p.53) 7 DATA REDUCTION AND PROBLEM KERNELS
Source:
Invitation to Fixed-Parameter Algorithms
Author(s):

Rolf Niedermeier

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566076.003.0007

This chapter presents one of the most basic and most important techniques for developing fixed-parameter algorithms: data reduction and problem kernelization. It starts with some basic definitions and facts, in particular defining the notion of reduction to a problem kernel (kernelization for short). After having presented some simple examples, the chapter continues with several specific kernelization results, including problem kernels for problems such as Maximum Satisfiability, Cluster Editing, Vertex Cover, 3-Hitting Set, and Dominating Set in Planar Graphs. The chapter concludes with some initial results on lower bounds for problem kernel sizes and a general summary.

Keywords:   kernelization, Cluster Editing, Vertex Cover, 3-Hitting Set, Dominating Set in Planar Graphs, lower bounds

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