Kernelization: Theory of Parameterized Preprocessing
Cambridge University Press, 1/10/2019
EAN 9781107057760, ISBN10: 1107057760
Hardcover, 500 pages, 23.5 x 15.7 x 3.1 cm
Language: English
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.