Downey Rod, Fellows Michael R. Fundamentals of parameterized complexity

Springer. 2013 — 787 pages.Contents.Parameterized Tractability.Preliminaries.
The Basic Definitions.Elementary Positive Techniques.Bounded Search Trees.
Kernelization.
More on Kernelization.
Iterative Compression, and Measure and Conquer, for Minimization Problems.
Further Elementary Techniques.
Color coding, Multilinear Detection, and Randomized divide-and-conquer.
Optimization Problems, Approximation Schemes, and Their Relation with FPT.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.Exotic Meta-Techniques.Well-Quasi-Orderings and the Robertson-Seymour Theorems.
The Graph Minor Theorem.
Applications of the Obstruction Principle and WQOs.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 Collapse.
Beyond W-Hardness.
k-Move Games.
Provable Intractability: The Class XP.
Another Basis.Approximations, Connections, Lower Bounds.The M-Hierarchy, and XP-optimality.
Kernelization Lower Bounds.Further Topics.Parameterized Approximation.
Parameterized Counting and Randomization.Appendices.Network Flows and Matchings.
Menger's Theorems.