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Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.Read more
- Can be used as a textbook, but also as a way for students to get the background to read current research in the area of approximation algorithms
- Explores the heuristic solution of discrete optimization problems
- Explains the principles of designing approximation algorithms, around algorithmic ideas that have been used in different ways and applied to different optimization problems
- Winner of the 2013 Lanchester Prize
Reviews & endorsements
"This is a beautifully written book that will bring anyone who reads it to the current frontiers of research in approximation algorithms. It covers everything from the classics to the latest, most exciting results such as ARV’s sparsest cut algorithm, and does so in an extraordinarily clear, rigorous and intuitive manner."
Anna Karlin, University of WashingtonSee more reviews
"The authors of this book are leading experts in the area of approximation algorithms. They do a wonderful job in providing clear and unified explanations of subjects ranging from basic and fundamental algorithmic design techniques to advanced results in the forefront of current research. This book will be very valuable to students and researchers alike."
Uriel Feige, Professor of Computer Science and Applied Mathematics, the Weizmann Institute
"Theory of approximation algorithms is one of the most exciting areas in theoretical computer science and operations research. This book, written by two leading researchers, systematically covers all the important ideas needed to design effective approximation algorithms. The description is lucid, extensive and up-to-date. This will become a standard textbook in this area for graduate students and researchers."
Toshihide Ibaraki, The Kyoto College of Graduate Studies for Informatics
"This book on approximation algorithms is a beautiful example of an ideal textbook. It gives a concise treatment of the major techniques, results and references in approximation algorithms and provides an extensive and systematic coverage of this topic up to the frontier of current research. It will become a standard textbook and reference for graduate students, teachers and researchers in the field."
Rolf H. Möhring, Technische Universität Berlin
"I have fond memories of learning approximation algorithms from an embryonic version of this book. The reader can expect a clearly written and thorough tour of all the important paradigms for designing efficient heuristics with provable performance guarantees for combinatorial optimization problems."
Tim Roughgarden, Stanford University
"This book is very well written. It could serve as a textbook on the design of approximation algorithms for discrete optimization problems. Readers will enjoy the clear and precise explanation of modern concepts, and the results obtained in this very elegant theory. Solving the exercises will benefit all readers interested in gaining a deeper understanding of the methods and results in the approximate algorithms for discrete optimization area."
Alexander Kreinin, Computing Reviews
"Any researcher interested in approximation algorithms would benefit greatly from this new book by Williamson and Schmoys. It is an ideal starting point for the fresh graduate student, as well as an excellent reference for the experts in the field. The wrting style is very clear and lucid, and it was a pleasure reading and reviewing this book."
Deeparnab Chakrabarty for SIGACT News
"The structure of the book is very interesting and allows a deeper understanding of the techniques presented. The whole book manages to develop a way of analyzing approximation algorithms and of designing approximation algorithms that perform well."
Dana Simian, Mathematical Reviews
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- Date Published: April 2011
- format: Hardback
- isbn: 9780521195270
- length: 518 pages
- dimensions: 262 x 189 x 34 mm
- weight: 1.12kg
- contains: 86 b/w illus. 121 exercises
- availability: Available
Table of Contents
Part I. An Introduction to the Techniques:
1. An introduction to approximation algorithms
2. Greedy algorithms and local search
3. Rounding data and dynamic programming
4. Deterministic rounding of linear programs
5. Random sampling and randomized rounding of linear programs
6. Randomized rounding of semidefinite programs
7. The primal-dual method
8. Cuts and metrics
Part II. Further Uses of the Techniques:
9. Further uses of greedy and local search algorithms
10. Further uses of rounding data and dynamic programming
11. Further uses of deterministic rounding of linear programs
12. Further uses of random sampling and randomized rounding of linear programs
13. Further uses of randomized rounding of semidefinite programs
14. Further uses of the primal-dual method
15. Further uses of cuts and metrics
16. Techniques in proving the hardness of approximation
17. Open problems
Appendix A. Linear programming
Appendix B. NP-completeness.
Instructors have used or reviewed this title for the following courses
- Algorithm Design
- Approximation Algorithms
- Computer Algorithms ll
- Design and Analysis of Algorithms
- Efficient Computing
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