Kernelization
Theory of Parameterized Preprocessing

A complete introduction to recent advances in preprocessing analysis, or kernelization, with extensive examples using a single data set.

Fedor V. Fomin (Author), Daniel Lokshtanov (Author), Saket Saurabh (Author), Meirav Zehavi (Author)

9781107057760, Cambridge University Press

Hardback, published 10 January 2019

528 pages
23.5 x 15.7 x 3.1 cm, 0.88 kg

'The book manages to present an incredible number of techniques, methods, and examples in its 528 pages. Each chapter ends with a bibliographic notes section, which often provides some small historical context for the material covered. It also points to more current results and papers although it does so very briefly. Together, this makes the textbook a valuable resource book to researchers.' Tim Jackman and Steve Homer, SIGACT News

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.

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.

Subject Areas: Algorithms & data structures [UMB], Optimization [PBU], Complex analysis, complex variables [PBKD]