Fundamentals of Parameterized Complexity

by Rodney G. Downey, Michael R. Fellows

Overview

This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.

Product Details

ISBN-13:	9781447155591
Publisher:	Springer-Verlag New York, LLC
Publication date:	12/03/2013
Series:	Texts in Computer Science
Sold by:	Barnes & Noble
Format:	eBook
File size:	6 MB

About the Author

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.

Table of Contents

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.

Editorial Reviews

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 breadthand 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)

From the Publisher