Kernelization : theory of parameterized preprocessing

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Bibliographic Information

Kernelization : theory of parameterized preprocessing

Fedor V. Fomin ... [et al.]

Cambridge University Press, 2019

  • : hbk

Available at  / 7 libraries

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Other authors: Daniel Lokshtanov, Saket Saurabh, Meirav Zehavi

Includes bibliographical references and index

DOI: 10.1017/9781107415157

Description and Table of Contents

Description

Preprocessing, or data reduction, is a standard technique for simplifying and speeding up computation. Written by a team of experts in the field, this book introduces a rapidly developing area of preprocessing analysis known as kernelization. The authors provide an overview of basic methods and important results, with accessible explanations of the most recent advances in the area, such as meta-kernelization, representative sets, polynomial lower bounds, and lossy kernelization. The text is divided into four parts, which cover the different theoretical aspects of the area: upper bounds, meta-theorems, lower bounds, and beyond kernelization. The methods are demonstrated through extensive examples using a single data set. Written to be self-contained, the book only requires a basic background in algorithmics and will be of use to professionals, researchers and graduate students in theoretical computer science, optimization, combinatorics, and related fields.

Table of Contents

  • 1. What is a kernel?
  • Part I. Upper Bounds: 2. Warm up
  • 3. Inductive priorities
  • 4. Crown decomposition
  • 5. Expansion lemma
  • 6. Linear programming
  • 7. Hypertrees
  • 8. Sunflower lemma
  • 9. Modules
  • 10. Matroids
  • 11. Representative families
  • 12. Greedy packing
  • 13. Euler's formula
  • Part II. Meta Theorems: 14. Introduction to treewidth
  • 15. Bidimensionality and protrusions
  • 16. Surgery on graphs
  • Part III. Lower Bounds: 17. Framework
  • 18. Instance selectors
  • 19. Polynomial parameter transformation
  • 20. Polynomial lower bounds
  • 21. Extending distillation
  • Part IV. Beyond Kernelization: 22. Turing kernelization
  • 23. Lossy kernelization.

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