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
3 - Polynomial-Time Reductions
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 notion of polynomial-time reductions. We explain how this technique can be used to transform an input for problem A to an input for problem B, mapping yes-instances for A to yes-instances for B and vice versa. If this transformation can be done in polynomial time, this implies that if B is polynomial-time computable, then so is A; also, it implies that if A has an exponential-time lower bound, then so must B. These polynomial-time reductions are thus a powerful technique to relate problems to each other. We will demonstrate several reduction strategies, namely reduction by restriction, by local replacement, and by component design. We include several exercises for practicing this technique.
- Type
- Chapter
- Information
- Cognition and IntractabilityA Guide to Classical and Parameterized Complexity Analysis, pp. 53 - 77Publisher: Cambridge University PressPrint publication year: 2019