Approximation algorithms and semidefinite programming

Approximation algorithms and semidefinite programming

by Gärtner, Bernd

Type Book
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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 cove…

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Title Statements

  • Full title :Approximation algorithms and semidefinite programming / Bernd Gärtner, Jiří Matoušek.

Summary

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

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Edition Statements

  • Publication Date:©2012.

Publication Statements

The Physical Object

  • Description:1 online resource (xi, 251 pages) : : illustrations

Edition Identifiers

  • ISBN:9783642220159, 3642220150, 3642220142, 9783642220142
  • DOI:10.1007/978-3-642-22015-9
  • oclc:ocn773812724
  • LC Classification:QA76.9.A43
  • Dewey Decimal:518/.1

Table of Contents

1. Introduction: MaxCut via semidefinite programming -- 2. Semidefinite programming -- 3. Shannon capacity and Lovász Theta -- 4. Duality and cone programming -- 5. Approximately solving semidefinite programs -- 6. An interior-point algorithm for semidefinite programming -- 7. Copositive programming -- 8. Lower bounds for the Goemans-Williamson MaxCut algorithm -- 9. Coloring 3-chromatic graphs -- 10. Maximizing a quadratic form on a graph -- 11. Colorings with low discrepancy -- 12. Constraint satisfaction problems, and relaxing them semidefinitely -- 13. Rounding via miniatures.

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Subjects

Algorithm Analysis and Problem Complexi… Algorithmes Algorithmes d'approximation ALGORITHMS Applications of Mathematics Approximation algorithms Computational complexity Computer software Discrete Mathematics in Computer Science Information theory Mathematical optimization mathematics Optimization Programmation (Mathématiques) Programmation semi-définie Semidefinite programming Theory of Computation

Writers

Gärtner, Bernd Matoušek, Jiří

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