Fundamentals of Parameterized Complexity (eBook)

Rodney G. Downey, Michael R. Fellows (Autoren)

eBook Download: PDF

2013 | 2013. Auflage
XXX, 763 Seiten
Springer London (Verlag)
978-1-4471-5559-1 (ISBN)

Infos

This text covers the state of the art in multivariate algorithmics and complexity, a vital field with countless applications in modern computing. It describes the latest methods of proving parameterized tractability, including powerful lower-bound techniques.

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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.

Autor

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.

Inhalt

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
The Basic 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

Produkt-Details

• Erscheint lt. Verlag: 3.12.2013
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Algorithmen
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 1-4471-5559-9 / 1447155599
• ISBN-13: 978-1-4471-5559-1 / 9781447155591