Overview
- 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
- Includes supplementary material: sn.pub/extras
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Table of contents (13 chapters)
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Front Matter
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(by Bernd Gärtner)
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Front Matter
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(by Jiřà Matoušek)
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Front Matter
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Back Matter
Keywords
About this book
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. Â
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.
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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.
Authors and Affiliations
Bibliographic Information
Book Title: Approximation Algorithms and Semidefinite Programming
Authors: Bernd Gärtner, Jiri Matousek
DOI: https://doi.org/10.1007/978-3-642-22015-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Hardcover ISBN: 978-3-642-22014-2Published: 13 January 2012
Softcover ISBN: 978-3-642-43332-0Published: 22 February 2014
eBook ISBN: 978-3-642-22015-9Published: 10 January 2012
Edition Number: 1
Number of Pages: XI, 251
Topics: Applications of Mathematics, Theory of Computation, Algorithm Analysis and Problem Complexity, Discrete Mathematics in Computer Science, Algorithms, Optimization