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Parameterized complexity [electronic resource] / R.G. Downey, M.R. Fellows.

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This monograph presents an approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking "k-slices" of the language. In doing so, the reader is introduced to new cla...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Downey, R. G. (Rod G.)
Other Authors: Fellows, M. R. (Michael Ralph), 1952-
Format: Electronic eBook
Language:English
Published: New York : Springer, ©1999.
Series:Monographs in computer science.
Subjects:
Computational complexity.
Table of Contents:
  • 1 Computers, Complexity, and Intractability from the Parametric Point of View
  • 1.1 Introduction
  • 1.2 The Role of Computational Complexity in Modern Science
  • 1.3 The Story of Dr. O, Continued
  • 1.4 Reworking the Foundations of Computational Complexity
  • 1.5 A Deal with the Devil
  • 1.6 How Parameters Arise in Practice
  • 1.7 A Distinctive Positive Toolkit
  • 1.8 O No?
  • 1.9 The Barometer of Parametric Intractability
  • 1.10 Structural Aspects of Parameterized Complexity
  • 1.11 An Overview of Current Research Horizons
  • I Parameterized Tractability
  • 2 The Basic Definitions
  • 3 Some Ad Hoc Methods: The Methods of Bounded Search Tree and Problem Kernel
  • 4 Optimization Problems, Approximation Schemes, and Their Relation with FPT
  • 5 The Advice View Revisited and LOGSPACE
  • 6 Methods via Automata and Bounded Treewidth
  • 7 Well-Quasi-Orderings and the Robertson-Seymour Theorems
  • 8 Miscellaneous Techniques
  • II Parameterized Intractability
  • 9 Reductions
  • 10 The Basic Class W[1] and an Analog of Cook's Theorem
  • 11 Some Other W[1]-Hardness Results
  • 12 The W -Hierarchy
  • 13 Beyond W[t]-Hardness
  • 14 Fixed Parameter Analogs of PSPACE and k-Move Games
  • 15 Provable Intractability: The Class XP
  • III Structural and Other Results
  • 16 Another Basis for the W -Hierarchy, the Tradeoff-Theorem, and Randomized Reductions
  • 17 Relationships with Classical Complexity and Limited Nondeterminism
  • 18 The Monotone and Antimonotone Collapse Theorems: MONOTONEW[2t + 1] = W[2t] and ANTIMONOTONEW[2t + 2] = W[2t + 1]
  • 19 The Structure of Languages Under Parameterized Reducibilities
  • IV Appendix
  • A A Problem Compendium and Guide to W-Hierarchy Completeness, Hardness, and Classification; and Some Research Horizons
  • B Research Horizons
  • B.2 A Lineup of Tough Customers
  • B.3 Connections Between Classical and Parameterized Complexity
  • B.4 Classification Gaps
  • B.5 Structural Issues and Analogs of Classical Results
  • References.

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