IntroductionPart I: Parameterized TractabilityPreliminariesThe Basic DefinitionsPart II: Elementary Positive TechniquesBounded Search TreesKernelizationMore on KernelizationIterative Compression, and Measure and Conquer, for Minimization ProblemsFurther Elementary TechniquesColour Coding, Multilinear Detection, and Randomized Divide and ConquerOptimization Problems, Approximation Schemes, and Their Relation to FPTPart III: Techniques Based on Graph StructureTreewidth and Dynamic ProgrammingHeuristics for TreewidthAutomata and Bounded TreewidthCourcelle's TheoremMore on Width-Metrics: Applications and Local TreewidthDepth-First Search and the Plehn-Voigt TheoremOther Width MetricsPart IV: Exotic Meta-TechniquesWell-Quasi-Orderings and the Robertson-Seymour TheoremsThe Graph Minor TheoremApplications of the Obstruction Principle and WQOsPart V: Hardness TheoryReductionsThe Basic Class W and an Analog of Cook's TheoremOther Hardness ResultsThe W-HierarchyThe Monotone and Antimonotone CollapsesBeyond W-Hardnessk-Move GamesProvable Intractability: The Class XPAnother BasisPart VI: Approximations, Connections, Lower BoundsThe M-Hierarchy, and XP-optimalityKernelization Lower BoundsPart VII: Further TopicsParameterized ApproximationParameterized Counting and RandomizationPart VIII: Research HorizonsResearch HorizonsPart IX AppendicesAppendix 1: Network Flows and MatchingsAppendix 2: Menger's Theorems
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.
"It is a new book that conveys a detailed picture of parameterized complexity as it stands today. ... The writing style is direct and engaging, allowing the reader to quickly grasp the core ideas for each topic. The book coverage is comprehensive, including even relatively recent results, and manages to give a rich representation of the current state of the field. In short, this is an excellent book that will serve well anyone interested in algorithm design and complexity." (Marius Zimand, zbMATH 1358.68006, 2017)"It can be read by graduate students who have some background in computational complexity. ... I strongly recommend Fundamentals of Parameterized Complexity for all researchers in theoretical computer science. ... It is my belief that this book is now the definitive text on parameterized complexity, both for the breadth and depth of material covered and also for including the latest developments in the field (as recently as 2012)." (Rajesh Chitnis, SIGACT News, Vol. 46 (1), 2015)"This book is currently the only monograph that covers lower bounds in kernelization or parameterized approximation. ... this new volume could serve as a (relatively easily) accessible source for a researcher in the area as well as helping students find their way into this interesting field. ... nearly 700 citations and a well-designed index help to navigate through the book and through the literature." (Henning Fernau, Mathematical Reviews, November, 2014)