Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Copyright Permissions
- 1 Introduction
- Part I Methods for Optimal Solutions
- Part II Methods for Near-optimal and Approximation Solutions
- 5 Branch-and-bound framework and application
- 6 Reformulation-Linearization Technique and applications
- 7 Linear approximation
- 8 Approximation algorithm and its applications – Part 1
- 9 Approximation algorithm and its applications – Part 2
- Part III Methods for Efficient Heuristic Solutions
- Part IV Other Topics
- References
- Index
8 - Approximation algorithm and its applications – Part 1
from Part II - Methods for Near-optimal and Approximation Solutions
Published online by Cambridge University Press: 05 May 2014
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Copyright Permissions
- 1 Introduction
- Part I Methods for Optimal Solutions
- Part II Methods for Near-optimal and Approximation Solutions
- 5 Branch-and-bound framework and application
- 6 Reformulation-Linearization Technique and applications
- 7 Linear approximation
- 8 Approximation algorithm and its applications – Part 1
- 9 Approximation algorithm and its applications – Part 2
- Part III Methods for Efficient Heuristic Solutions
- Part IV Other Topics
- References
- Index
Summary
Do not follow where the path may lead. Go, instead, where there is no path and leave a trail.
Ralph Waldo EmersonReview of approximation algorithms
Recall that Part II of this book focuses on methods for near-optimal and approximation solutions. Specifically, Chapters 5 to 7 follow the OR optimization approach to develop a (1 − ∊)-optimal solution. In this and the following chapters, we will show how to develop the (1 − ∊)-optimal solution by following the CS algorithm design approach.
We first give a brief overview of the so-called approximation algorithms. Such algorithms are designed to offer solutions that can approximate the unknown optimal solution according to certain benchmark performance criteria. In particular, in wireless network research, the most popular approximation algorithms can be classified as constant-factor approximation algorithms and (1 − ∊)-optimal approximation algorithms.
• Constant-factor approximation algorithms. We use a maximization problem with a positive optimal objective value OPT (unknown) as an example. If we can prove that the obtained feasible solution achieves an objective value that is at least c · OPT, where c < 1 is a constant, then the designed algorithm is a constant-factor approximation algorithm. Likewise, for a minimization problem, if we can prove that the obtained feasible solution achieves an objective value that is at most c · OPT, where c > 1 is a constant, then the designed algorithm is a constant-factor approximation algorithm.
- Type
- Chapter
- Information
- Applied Optimization Methods for Wireless Networks , pp. 191 - 210Publisher: Cambridge University PressPrint publication year: 2014