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The Design of Approximation Algorithms

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  • Date Published: April 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521195270

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About the Authors
  • 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.

    • 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
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    • 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 Washington

    "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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    Product details

    • 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
  • Authors

    David P. Williamson, Cornell University, New York
    David P. Williamson is a Professor at Cornell University with a joint appointment in the School of Operations Research and Information Engineering and in the Department of Information Science. Prior to joining Cornell, he was a Research Staff Member at the IBM T. J. Watson Research Center and a Senior Manager at the IBM Almaden Research Center. He has won several awards for his work on approximation algorithms, including the 2000 Fulkerson Prize, sponsored by the American Mathematical Society and the Mathematical Programming Society. He has served on several editorial boards, including ACM Transactions on Algorithms, Mathematics of Operations Research, the SIAM Journal on Computing and the SIAM Journal on Discrete Mathematics.

    David B. Shmoys, Cornell University, New York
    David Shmoys has faculty appointments in both the School of Operations Research and Information Engineering and the Department of Computer Science, and he is currently Associate Director of the Institute for Computational Sustainability at Cornell University. He is a Fellow of the ACM, was an NSF Presidential Young Investigator, and has served on numerous editorial boards, including Mathematics of Operations Research (for which he is currently an associate editor), Operations Research, the ORSA Journal on Computing, Mathematical Programming and both the SIAM Journal on Computing and the SIAM Journal on Discrete Mathematics; he also served as editor-in-chief for the latter.


    • Winner of the 2013 Lanchester Prize

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