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.
Author(s): Rodney G. Downey, Michael R. Fellows
Series: Texts in Computer Science
Publisher: Springer
Year: 2013
Language: English
Pages: 765
Tags: Algorithm Analysis and Problem Complexity; Mathematics of Algorithmic Complexity
Front Matter....Pages I-XXX
Front Matter....Pages 1-1
Preliminaries....Pages 3-13
The Basic Definitions....Pages 15-21
Front Matter....Pages 23-23
Bounded Search Trees....Pages 25-47
Kernelization....Pages 49-89
More on Kernelization....Pages 91-106
Iterative Compression, and Measure and Conquer, for Minimization Problems....Pages 107-130
Further Elementary Techniques....Pages 131-141
Color Coding, Multilinear Detection, and Randomized Divide and Conquer....Pages 143-170
Optimization Problems, Approximation Schemes, and Their Relation to FPT ....Pages 171-182
Front Matter....Pages 183-183
Treewidth and Dynamic Programming....Pages 185-203
Heuristics for Treewidth....Pages 205-211
Methods via Automata and Bounded Treewidth....Pages 213-264
Courcelle’s Theorem....Pages 265-278
More on Width-Metrics: Applications and Local Treewidth....Pages 279-289
Depth-First Search and the Plehn–Voigt Theorem....Pages 291-300
Other Width Metrics....Pages 301-316
Front Matter....Pages 317-317
Well-Quasi-Orderings and the Robertson–Seymour Theorems....Pages 319-338
The Graph Minor Theorem....Pages 339-350
Applications of the Obstruction Principle and WQO s....Pages 351-372
Front Matter....Pages 373-373
Reductions....Pages 375-382
Front Matter....Pages 373-373
The Basic Class W [1] and an Analog of Cook’s Theorem....Pages 383-406
Some Other W [1] Hardness Results....Pages 407-426
The W -Hierarchy....Pages 427-459
The Monotone and Antimonotone Collapse Theorems: Monotone W [2 t +1]= W [2 t ] and Antimonotone W [2 t +2]= W [2 t +1]....Pages 461-471
Beyond W [ t ]-Hardness....Pages 473-489
Fixed Parameter Analogues of PSpace and k -Move Games....Pages 491-507
Provable Intractability: The Class XP....Pages 509-519
Another Basis for the W -Hierarchy and the Tradeoff Theorem....Pages 521-531
Front Matter....Pages 533-533
The M -Hierarchy, and XP -Optimality....Pages 535-570
Kernelization Lower Bounds....Pages 571-619
Front Matter....Pages 621-621
Parameterized Approximation....Pages 623-644
Parameterized Counting and Randomization....Pages 645-673
Front Matter....Pages 675-675
Research Horizons....Pages 677-686
Front Matter....Pages 687-687
Appendix 1: Network Flows and Matchings....Pages 689-704
Appendix 2: Menger’s Theorems....Pages 705-707
Back Matter....Pages 709-763
