Fundamentals of Parameterized Complexity (eBook)

Dr. Rodney G. Downey is a Professor in the School of Mathematics, Statistics and Operations Research, at the Victoria University of Wellington, New Zealand. Dr. Michael R. Fellows is a Professor in the School of Engineering and Information Technology, at the Charles Darwin University, Darwin, NT, Australia.

Introduction
Part I: Parameterized Tractability
Preliminaries
The Basic Definitions
Part II: Elementary Positive Techniques
Bounded Search Trees
Kernelization
More on Kernelization
Iterative Compression, and Measure and Conquer, for Minimization Problems
Further Elementary Techniques
Colour Coding, Multilinear Detection, and Randomized Divide and Conquer
Optimization Problems, Approximation Schemes, and Their Relation to FPT
Part III: Techniques Based on Graph Structure
Treewidth and Dynamic Programming
Heuristics for Treewidth
Automata and Bounded Treewidth
Courcelle's Theorem
More on Width-Metrics: Applications and Local Treewidth
Depth-First Search and the Plehn-Voigt Theorem
Other Width Metrics
Part IV: Exotic Meta-Techniques
Well-Quasi-Orderings and the Robertson-Seymour Theorems
The Graph Minor Theorem
Applications of the Obstruction Principle and WQOs
Part V: Hardness Theory
Reductions
The Basic Class W[1] and an Analog of Cook's Theorem
Other Hardness Results
The W-Hierarchy
The Monotone and Antimonotone Collapses
Beyond W-Hardness
k-Move Games
Provable Intractability: The Class XP
Another Basis
Part VI: Approximations, Connections, Lower Bounds
The M-Hierarchy, and XP-optimality
Kernelization Lower Bounds
Part VII: Further Topics
Parameterized Approximation
Parameterized Counting and Randomization
Part VIII: Research Horizons
Research Horizons
Part IX Appendices
Appendix 1: Network Flows and Matchings
Appendix 2: Menger's Theorems