Fundamentals of Parameterized Complexity
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Beschreibung
The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society.
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.
Topics and 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
This classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research.
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.
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: sn.pub/extras
Autor*in
Rodney G. Downey
Themen in »Fundamentals of Parameterized Complexity«
Computational Complexity Graph Theory Hardness Theory Kernelization Lower Bounds Multivariate Algorithmics Parameterized Tractability algorithm analysis and problem complexity algorithmic complexity
Stimmen zu »Fundamentals of Parameterized Complexity«
“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)()