Approximation Algorithms and Semidefinite Programming

Authors: Gärtner, Bernd, Matousek, Jiri

  • First textbook treatment of an often-taught topic
  • Combines in-depth treatment of classical material with coverage of very recent developments
  • Every chapter comes with an extensive list of exercises
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About this Textbook

Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material.  

There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms.

 

This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.

Table of contents (13 chapters)

  • Introduction: MaxCut Via Semidefinite Programming

    Gärtner, Bernd (et al.)

    Pages 3-14

  • Semidefinite Programming

    Gärtner, Bernd (et al.)

    Pages 15-25

  • Shannon Capacity and Lovász Theta

    Gärtner, Bernd (et al.)

    Pages 27-43

  • Duality and Cone Programming

    Gärtner, Bernd (et al.)

    Pages 45-73

  • Approximately Solving Semidefinite Programs

    Gärtner, Bernd (et al.)

    Pages 75-98

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-22015-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-3-642-22014-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.95
price for USA
  • ISBN 978-3-642-43332-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Approximation Algorithms and Semidefinite Programming
Authors
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-22015-9
DOI
10.1007/978-3-642-22015-9
Hardcover ISBN
978-3-642-22014-2
Softcover ISBN
978-3-642-43332-0
Edition Number
1
Number of Pages
XI, 251
Topics