Approximation Algorithms and Semidefinite Programming

  • Bernd Gärtner
  • Jiri Matousek

Table of contents

  1. Front Matter
    Pages i-xi
  2. (by Bernd Gärtner)

    1. Front Matter
      Pages 1-1
    2. Bernd Gärtner, Jiří Matoušek
      Pages 3-14
    3. Bernd Gärtner, Jiří Matoušek
      Pages 15-25
    4. Bernd Gärtner, Jiří Matoušek
      Pages 27-43
    5. Bernd Gärtner, Jiří Matoušek
      Pages 45-73
    6. Bernd Gärtner, Jiří Matoušek
      Pages 75-98
    7. Bernd Gärtner, Jiří Matoušek
      Pages 99-118
    8. Bernd Gärtner, Jiří Matoušek
      Pages 119-130
  3. (by Jiří Matoušek)

    1. Front Matter
      Pages 131-131
    2. Bernd Gärtner, Jiří Matoušek
      Pages 133-155
    3. Bernd Gärtner, Jiří Matoušek
      Pages 157-166
    4. Bernd Gärtner, Jiří Matoušek
      Pages 167-177
    5. Bernd Gärtner, Jiří Matoušek
      Pages 179-191
    6. Bernd Gärtner, Jiří Matoušek
      Pages 193-210
    7. Bernd Gärtner, Jiří Matoušek
      Pages 211-227
  4. Back Matter
    Pages 229-251

About this book

Introduction

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.

Keywords

approximation algorithms semidefinite programming

Authors and affiliations

  • Bernd Gärtner
    • 1
  • Jiri Matousek
    • 2
  1. 1.Institute of, Theoretical Computer ScienceETH ZurichZurichSwitzerland
  2. 2.Dept. Applied MathematicsCharles UniversityPrague 1Czech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22015-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-22014-2
  • Online ISBN 978-3-642-22015-9
  • About this book