Approximation Algorithms and Semidefinite Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation Algorithms and Semidefinite Programming write by Bernd Gärtner. This book was released on 2012-01-10. Approximation Algorithms and Semidefinite Programming available in PDF, EPUB and Kindle. 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.
Aspects of Semidefinite Programming
Aspects of Semidefinite Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Aspects of Semidefinite Programming write by E. de Klerk. This book was released on 2002-03-31. Aspects of Semidefinite Programming available in PDF, EPUB and Kindle. Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming. In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson. Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.
Aspects of Semidefinite Programming
Aspects of Semidefinite Programming - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Aspects of Semidefinite Programming write by E. de Klerk. This book was released on 2006-04-18. Aspects of Semidefinite Programming available in PDF, EPUB and Kindle. Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming. In this monograph the basic theory of interior point algorithms is explained. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the Lovász theta function and the MAX-CUT approximation algorithm by Goemans and Williamson. Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.
The Design of Approximation Algorithms
The Design of Approximation Algorithms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Design of Approximation Algorithms write by David P. Williamson. This book was released on 2011-04-26. The Design of Approximation Algorithms available in PDF, EPUB and Kindle. Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
Approximation Algorithms for NP-hard Problems
Approximation Algorithms for NP-hard Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation Algorithms for NP-hard Problems write by Dorit S. Hochbaum. This book was released on 1997. Approximation Algorithms for NP-hard Problems available in PDF, EPUB and Kindle. This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms. Among the techniques discussed: the use of linear programming, primal-dual techniques in worst-case analysis, semidefinite programming, computational geometry techniques, randomized algorithms, average-case analysis, probabilistically checkable proofs and inapproximability, and the Markov Chain Monte Carlo method. The text includes a variety of pedagogical features: definitions, exercises, open problems, glossary of problems, index, and notes on how best to use the book.
