Book contents
- Frontmatter
- Contents
- List of Figures
- List of Tables
- Preface
- Part I Introduction
- Part II Concepts and Techniques
- 2 Polynomial versus Exponential Time
- 3 Polynomial-Time Reductions
- 4 Classical Complexity Classes
- 5 Fixed-Parameter Tractable Time
- 6 Parameterized Reductions
- 7 Parameterized Complexity Classes
- Part III Reflections and Elaborations
- Part IV Applications
- Appendix A Mathematical Background
- Appendix B List of Computational Problems
- Appendix C Compendium of Complexity Results
- References
- Index
5 - Fixed-Parameter Tractable Time
from Part II - Concepts and Techniques
Published online by Cambridge University Press: 18 April 2019
- Frontmatter
- Contents
- List of Figures
- List of Tables
- Preface
- Part I Introduction
- Part II Concepts and Techniques
- 2 Polynomial versus Exponential Time
- 3 Polynomial-Time Reductions
- 4 Classical Complexity Classes
- 5 Fixed-Parameter Tractable Time
- 6 Parameterized Reductions
- 7 Parameterized Complexity Classes
- Part III Reflections and Elaborations
- Part IV Applications
- Appendix A Mathematical Background
- Appendix B List of Computational Problems
- Appendix C Compendium of Complexity Results
- References
- Index
Summary
In this chapter, we introduce the concepts of parameterized problem and fixed-parameter tractability. Using these concepts, one can show that problems that are polynomial-time intractable in general (i.e., \np-hard) may yet be practically solvable provided only that certain input parameters are constrained in terms of their values. This conception of tractability underlies the FPT-Cognition Thesis introduced in Chapter 1. We illustrate three techniques for showing that a parameterized problem is fixed-parameter tractable, namely, brute-force combinatorics, bounded search trees, and reduction to a problem kernel.We also include several exercises for practicing these techniques.
- Type
- Chapter
- Information
- Cognition and IntractabilityA Guide to Classical and Parameterized Complexity Analysis, pp. 108 - 127Publisher: Cambridge University PressPrint publication year: 2019