Fundamentals of Parameterized Complexity

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.