Dr. Rodney G. Downeyis 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.

Presents an accessible overview of the state of the art of multivariate algorithmics and complexity

Describes the wealth of recent techniques for proving parameterized tractability

Showcases the powerful new lower bound techniques

Includes supplementary material: [...]

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.- TheBasic 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.