Approximation Algorithms and Semidefinite Programming
Authors: Gärtner, Bernd, Matousek, Jiri
Free Preview- 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
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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)
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Introduction: MaxCut Via Semidefinite Programming
Pages 3-14
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Semidefinite Programming
Pages 15-25
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Shannon Capacity and Lovász Theta
Pages 27-43
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Duality and Cone Programming
Pages 45-73
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Approximately Solving Semidefinite Programs
Pages 75-98
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Table of contents (13 chapters)
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- Download Sample pages 2 PDF (196.9 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Approximation Algorithms and Semidefinite Programming
- Authors
-
- Bernd Gärtner
- Jiri Matousek
- 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
