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The Design of Approximation Algorithms

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

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  • Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. 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 section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses, it 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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    Awards

    • Winner of the 2013 Lanchester Prize

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    Product details

    • Date Published: June 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.

    Awards

    • Winner of the 2013 Lanchester Prize

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