Approximation Algorithms and Semidefinite Programming
Approximation Algorithms and Semidefinite Programming

Author: Bernd Gärtner

Publisher: Springer Science & Business Media

Published: 2012-01-10

Total Pages: 253

ISBN-13: 3642220150

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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.

The Design of Approximation Algorithms
The Design of Approximation Algorithms

Author: David P. Williamson

Publisher: Cambridge University Press

Published: 2011-04-26

Total Pages: 517

ISBN-13: 1139498177

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Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. 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 section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses, it will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

Algorithms and Computation
Algorithms and Computation

Author: Ying Fei Dong

Publisher: Springer

Published: 2009-12-04

Total Pages: 1246

ISBN-13: 3642106315

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This book constitutes the refereed proceedings of the 20th International Symposium on Algorithms and Computation, ISAAC 2009, held in Honolulu, Hawaii, USA in December 2009. The 120 revised full papers presented were carefully reviewed and selected from 279 submissions for inclusion in the book. This volume contains topics such as algorithms and data structures, approximation algorithms, combinatorial optimization, computational biology, computational complexity, computational geometry, cryptography, experimental algorithm methodologies, graph drawing and graph algorithms, internet algorithms, online algorithms, parallel and distributed algorithms, quantum computing and randomized algorithms.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author: Anupam Gupta

Publisher: Springer

Published: 2012-07-20

Total Pages: 687

ISBN-13: 3642325122

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This book constitutes the joint refereed proceedings of the 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012, and the 16th International Workshop on Randomization and Computation, RANDOM 2012, held in Cambridge, Massachusetts, USA, in August 2011. The volume contains 28 contributed papers, selected by the APPROX Program Committee out of 70 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 67 submissions. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

Automata, Languages, and Programming
Automata, Languages, and Programming

Author: Artur Czumaj

Publisher: Springer

Published: 2012-06-23

Total Pages: 889

ISBN-13: 3642315941

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This two-volume set of LNCS 7391 and LNCS 7392 constitutes the refereed proceedings of the 39th International Colloquium on Automata, Languages and Programming, ICALP 2012, held in Warwick, UK, in July 2012. The total of 123 revised full papers presented in this volume were carefully reviewed and selected from 432 submissions. They are organized in three tracks focussing on algorithms, complexity and games; logic, semantics, automata and theory of programming; and foundations of networked computation.

Issues in Computation: 2011 Edition
Issues in Computation: 2011 Edition

Author:

Publisher: ScholarlyEditions

Published: 2012-01-09

Total Pages: 1318

ISBN-13: 146496453X

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Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author: Maria Serna

Publisher: Springer Science & Business Media

Published: 2010-08-19

Total Pages: 794

ISBN-13: 3642153682

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This book constitutes the joint refereed proceedings of the 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010, and the 14th International Workshop on Randomization and Computation, RANDOM 2010, held in Barcelona, Spain, in September 2010. The 28 revised full papers of the APPROX 2010 workshop and the 29 revised full papers of the RANDOM 2010 workshop included in this volume, were carefully reviewed and selected from 66 and 61 submissions, respectively. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

The Design of Approximation Algorithms
The Design of Approximation Algorithms

Author: David P. Williamson

Publisher: Cambridge University Press

Published: 2011-04-26

Total Pages: 518

ISBN-13: 9780521195270

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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.

Mathematics and Computation
Mathematics and Computation

Author: Avi Wigderson

Publisher: Princeton University Press

Published: 2019-10-29

Total Pages: 434

ISBN-13: 0691189137

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From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Handbook on Semidefinite, Conic and Polynomial Optimization
Handbook on Semidefinite, Conic and Polynomial Optimization

Author: Miguel F. Anjos

Publisher: Springer Science & Business Media

Published: 2011-11-19

Total Pages: 955

ISBN-13: 1461407699

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Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.