Approximation Algorithms And Semidefinite Programming
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Approximation Algorithms And Semidefinite Programming
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Author : Bernd Gärtner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-10
Approximation Algorithms And Semidefinite Programming written by Bernd Gärtner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-10 with Mathematics categories.
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
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Author : E. de Klerk
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Aspects Of Semidefinite Programming written by E. de Klerk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Computers categories.
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.
An Introduction To Semidefinite Programming And Its Applications To Approximation Algorithms
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Author : Thomas Hofmeister
language : en
Publisher:
Release Date : 1997
An Introduction To Semidefinite Programming And Its Applications To Approximation Algorithms written by Thomas Hofmeister and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
The Design Of Approximation Algorithms
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Author : David P. Williamson
language : en
Publisher: Cambridge University Press
Release Date : 2011-04-26
The Design Of Approximation Algorithms written by David P. Williamson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-26 with Computers categories.
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.
On The Optimality Of Some Semidefinite Programming Based Approximation Algorithms Under The Unique Games Conjecture
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Author : Seth R. Flaxman
language : en
Publisher:
Release Date : 2008
On The Optimality Of Some Semidefinite Programming Based Approximation Algorithms Under The Unique Games Conjecture written by Seth R. Flaxman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Lectures On Proof Verification And Approximation Algorithms
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Author : Ernst W. Mayr
language : en
Publisher: Springer
Release Date : 2006-06-08
Lectures On Proof Verification And Approximation Algorithms written by Ernst W. Mayr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-08 with Computers categories.
During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques
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Author : Chandra Chekuri
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-08
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques written by Chandra Chekuri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-08 with Computers categories.
This book constitutes the joint refereed proceedings of the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and the 9th International Workshop on Randomization and Computation, RANDOM 2005, held in Berkeley, CA, USA in August 2005. The volume contains 41 carefully reviewed papers, selected by the two program committees from a total of 101 submissions. Among the issues addressed are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of approximation and randomness.
Integer Programming And Combinatorial Optimization
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Author : Karen Aardal
language : en
Publisher: Springer
Release Date : 2003-06-29
Integer Programming And Combinatorial Optimization written by Karen Aardal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-29 with Mathematics categories.
This volume contains the papers selected for presentation at IPCO VIII, the Eighth Conference on Integer Programming and Combinatorial Optimization, Utrecht, The Netherlands, 2001. This meeting isa forum for researchers and practitioners working on various aspects of integer programming and combi- torial optimization. The aim is to present recent developments in theory, com- tation, and application of integer programming and combinatorial optimization. Topics include, but are not limited to: approximation algorithms, branch and bound algorithms, computational biology, computational complexity, compu- tional geometry, cutting plane algorithms, diophantine equations, geometry of numbers, graph and network algorithms, integer programming, matroids and submodular functions, on-line algorithms, polyhedral combinatorics, scheduling theory and algorithms, and semide nit e programs. IPCO was established in 1988 when the rs t IPCO program committee was formed. The locations and years of the seven rs t IPCO conferences were: IPCO I, Waterloo (Canada) 1990, IPCO II, Pittsburgh (USA) 1992, IPCO III, - ice (Italy) 1993, IPCO IV, Copenhagen (Denmark) 1995, IPCO V, Vancouver (Canada) 1996, IPCO VI, Houston (USA) 1998, IPCO VII, Graz (Austria) 1999. IPCO is held every year in which no MPS (Mathematical Programming Society) International Symposium takes place. Since the MPS meeting is triennial, IPCO conferences are held twice in every three-year period. Asa rule, IPCO is held somewhere in Northern America in even years, and somewhere in Europe in odd years.
Approximation Algorithms For Combinatorial Optimization
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Author : Klaus Jansen
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-07
Approximation Algorithms For Combinatorial Optimization written by Klaus Jansen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07 with Computers categories.
Computer simulation has become a basic tool in many branches of physics such as statistical physics, particle physics, or materials science. The application of efficient algorithms is at least as important as good hardware in large-scale computation. This volume contains didactic lectures on such techniques based on physical insight. The emphasis is on Monte Carlo methods (introduction, cluster algorithms, reweighting and multihistogram techniques, umbrella sampling), efficient data analysis and optimization methods, but aspects of supercomputing, the solution of stochastic differential equations, and molecular dynamics are also discussed. The book addresses graduate students and researchers in theoretical and computational physics.
Approximation Algorithms For Combinatorial Optimization
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Author : Klaus Jansen
language : en
Publisher: Springer
Release Date : 2003-06-30
Approximation Algorithms For Combinatorial Optimization written by Klaus Jansen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Computers categories.
This book constitutes the refereed proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, held in Rome, Italy in September 2002. The 20 revised full papers presented were carefully reviewed and selected from 54 submissions. Among the topics addressed are design and analysis of approximation algorithms, inapproximability results, online problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and other fields.