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The Design of Approximation Algorithms

The Design of Approximation Algorithms Author David P. Williamson
ISBN-10 9781139498173
Release 2011-04-26
Pages
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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.



The Design of Approximation Algorithms

The Design of Approximation Algorithms Author David P. Williamson
ISBN-10 0521195276
Release 2011-04-26
Pages 518
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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.



The Design of Approximation Algorithms

The Design of Approximation Algorithms Author David P. Williamson
ISBN-10 1139077759
Release 2014-05-14
Pages 518
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Designed as a textbook for graduate courses on algorithms, this book presents efficient algorithms that find provably near-optimal solutions.



Approximation Algorithms

Approximation Algorithms Author Vijay V. Vazirani
ISBN-10 9783662045657
Release 2013-03-14
Pages 380
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Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.



Design and Analysis of Approximation Algorithms

Design and Analysis of Approximation Algorithms Author Ding-Zhu Du
ISBN-10 9781461417019
Release 2011-11-18
Pages 440
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This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way.



Handbook of Approximation Algorithms and Metaheuristics

Handbook of Approximation Algorithms and Metaheuristics Author Teofilo F. Gonzalez
ISBN-10 1420010743
Release 2007-05-15
Pages 1432
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Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis. Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems.



Approximation Algorithms for NP hard Problems

Approximation Algorithms for NP hard Problems Author Dorit S. Hochbaum
ISBN-10 0534949681
Release 1997
Pages 596
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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.



Approximation Algorithms and Semidefinite Programming

Approximation Algorithms and Semidefinite Programming Author Bernd Gärtner
ISBN-10 9783642220159
Release 2012-01-10
Pages 251
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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.



Randomized Algorithms

Randomized Algorithms Author Rajeev Motwani
ISBN-10 9781139643139
Release 1995-08-25
Pages
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For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.



The Design of Competitive Online Algorithms Via a Primal Dual Approach

The Design of Competitive Online Algorithms Via a Primal Dual Approach Author Niv Buchbinder
ISBN-10 9781601982162
Release 2009
Pages 176
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Extends the primal-dual method to the setting of online algorithms, and shows its applicability to a wide variety of fundamental problems.



Geometric Approximation Algorithms

Geometric Approximation Algorithms Author Sariel Har-Peled
ISBN-10 9780821849118
Release 2011
Pages 362
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Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.



Algorithmics for Hard Problems

Algorithmics for Hard Problems Author Juraj Hromkovič
ISBN-10 9783662046166
Release 2013-03-14
Pages 494
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An introduction to the methods of designing algorithms for hard computing tasks, concentrating mainly on approximate, randomized, and heuristic algorithms, and on the theoretical and experimental comparison of these approaches according to the requirements of the practice. This is the first book to systematically explain and compare all the main possibilities of attacking hard computing problems. It also closes the gap between theory and practice by providing at once a graduate textbook and a handbook for practitioners dealing with hard computing problems.



Approximation Algorithms for Combinatorial Optimization

Approximation Algorithms for Combinatorial Optimization Author Klaus Jansen
ISBN-10 9783540444367
Release 2003-07-31
Pages 282
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Approximation Algorithms for Combinatorial Optimization has been writing in one form or another for most of life. You can find so many inspiration from Approximation Algorithms for Combinatorial Optimization also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Approximation Algorithms for Combinatorial Optimization book for free.



The Algorithm Design Manual

The Algorithm Design Manual Author Steven S Skiena
ISBN-10 9781848000704
Release 2009-04-05
Pages 730
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This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: • Doubles the tutorial material and exercises over the first edition • Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video • Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them • Includes several NEW "war stories" relating experiences from real-world applications • Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java



Greedy Approximation

Greedy Approximation Author Vladimir Temlyakov
ISBN-10 9781139502801
Release 2011-09-08
Pages
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This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.



DESIGN METHODS AND ANALYSIS OF ALGORITHMS

DESIGN METHODS AND ANALYSIS OF ALGORITHMS Author S. K. BASU
ISBN-10 9788120347465
Release 2013-04-17
Pages 400
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The design of correct and efficient algorithms for problem solving lies at the heart of computer science. This concise text, without being highly specialized, teaches the skills needed to master the essentials of this subject. With clear explanations and engaging writing style, the book places increased emphasis on algorithm design techniques rather than programming in order to develop in the reader the problem-solving skills. The treatment throughout the book is primarily tailored to the curriculum needs of B.Tech. students in computer science and engineering, B.Sc. (Hons.) and M.Sc. students in computer science, and MCA students. The book focuses on the standard algorithm design methods and the concepts are illustrated through representative examples to offer a reader-friendly text. Elementary analysis of time complexities is provided for each example-algorithm. A varied collection of exercises at the end of each chapter serves to reinforce the principles/methods involved. New To This Edition • Additional problems • A new Chapter 14 on Bioinformatics Algorithms • The following new sections: » BSP model (Chapter 0) » Some examples of average complexity calculation (Chapter 1) » Amortization (Chapter 1) » Some more data structures (Chapter 1) » Polynomial multiplication (Chapter 2) » Better-fit heuristic (Chapter 7) » Graph matching (Chapter 9) » Function optimization, neighbourhood annealing and implicit elitism (Chapter 12) • Additional matter in Chapter 15 • Appendix



Spanning Trees and Optimization Problems

Spanning Trees and Optimization Problems Author Bang Ye Wu
ISBN-10 0203497287
Release 2004-01-27
Pages 200
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The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under one cover spanning tree properties, classical results, and recent research developments. Spanning Trees and Optimization Problems offers the first complete treatment of spanning tree algorithms, from their role in classical computer science to their most modern applications. The authors first explain the general properties of spanning trees, then focus on three main categories: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. Along with the theoretical descriptions of the methods, numerous examples and applications illustrate the concepts in practice. The final chapter explores several other interesting spanning trees, including maximum leaf spanning trees, minimum diameter spanning trees, Steiner trees, and evolutionary trees. With logical organization, well chosen topics, and easy to understand pseudocode, the authors provide not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. This book will be a welcome addition to your reference shelf whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems