Algorithms For Approximation

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The Design of Approximation Algorithms

David P. Williamson,David B. Shmoys
The Design of Approximation Algorithms Book PDF

Author : David P. Williamson,David B. Shmoys
Publisher : Cambridge University Press
Page : 518 pages
File Size : 55,6 Mb
Release : 2011-04-26
Category : Computers
ISBN : 0521195276

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The Design of Approximation Algorithms by David P. Williamson,David B. Shmoys Pdf

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

Vijay V. Vazirani
Approximation Algorithms Book PDF

Author : Vijay V. Vazirani
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 47,5 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9783662045657

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Approximation Algorithms by Vijay V. Vazirani Pdf

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.

Geometric Approximation Algorithms

Sariel Har-Peled
Geometric Approximation Algorithms Book PDF

Author : Sariel Har-Peled
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 54,6 Mb
Release : 2011
Category : Computers
ISBN : 9780821849118

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Geometric Approximation Algorithms by Sariel Har-Peled Pdf

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.

Approximation Algorithms and Semidefinite Programming

Bernd Gärtner,Jiri Matousek
Approximation Algorithms and Semidefinite Programming Book PDF

Author : Bernd Gärtner,Jiri Matousek
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 54,9 Mb
Release : 2012-01-10
Category : Mathematics
ISBN : 9783642220159

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Approximation Algorithms and Semidefinite Programming by Bernd Gärtner,Jiri Matousek Pdf

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.

Approximation and Optimization

Ioannis C. Demetriou,Panos M. Pardalos
Approximation and Optimization Book PDF

Author : Ioannis C. Demetriou,Panos M. Pardalos
Publisher : Springer
Page : 237 pages
File Size : 42,7 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9783030127671

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Approximation and Optimization by Ioannis C. Demetriou,Panos M. Pardalos Pdf

This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

Design and Analysis of Approximation Algorithms

Ding-Zhu Du,Ker-I Ko,Xiaodong Hu
Design and Analysis of Approximation Algorithms Book PDF

Author : Ding-Zhu Du,Ker-I Ko,Xiaodong Hu
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 40,9 Mb
Release : 2011-11-18
Category : Mathematics
ISBN : 9781461417019

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Design and Analysis of Approximation Algorithms by Ding-Zhu Du,Ker-I Ko,Xiaodong Hu Pdf

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

Teofilo F. Gonzalez
Handbook of Approximation Algorithms and Metaheuristics Book PDF

Author : Teofilo F. Gonzalez
Publisher : CRC Press
Page : 840 pages
File Size : 49,9 Mb
Release : 2018-05-15
Category : Computers
ISBN : 9781351236409

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Handbook of Approximation Algorithms and Metaheuristics by Teofilo F. Gonzalez Pdf

Handbook of Approximation Algorithms and Metaheuristics, Second Edition reflects the tremendous growth in the field, over the past two decades. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability. Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks (sensor and wireless), communication, bioinformatics search, streams, virtual communities, and more. About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph.D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma, the Pennsylvania State University, and the University of Texas at Dallas, before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.

Approximation Algorithms for NP-hard Problems

Dorit S. Hochbaum
Approximation Algorithms for NP hard Problems Book PDF

Author : Dorit S. Hochbaum
Publisher : Course Technology
Page : 632 pages
File Size : 54,5 Mb
Release : 1997
Category : Computers
ISBN : UOM:39015058079271

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Approximation Algorithms for NP-hard Problems by Dorit S. Hochbaum Pdf

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.

Stochastic Approximation and Recursive Algorithms and Applications

Harold Kushner,G. George Yin
Stochastic Approximation and Recursive Algorithms and Applications Book PDF

Author : Harold Kushner,G. George Yin
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 44,7 Mb
Release : 2006-05-04
Category : Mathematics
ISBN : 9780387217697

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Stochastic Approximation and Recursive Algorithms and Applications by Harold Kushner,G. George Yin Pdf

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.

Approximation and Online Algorithms

Jochen Koenemann,Britta Peis
Approximation and Online Algorithms Book PDF

Author : Jochen Koenemann,Britta Peis
Publisher : Springer Nature
Page : 286 pages
File Size : 52,8 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030927028

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Approximation and Online Algorithms by Jochen Koenemann,Britta Peis Pdf

This book constitutes the thoroughly refereed workshop post-proceedings of the 19th International Workshop on Approximation and Online Algorithms, WAOA 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 16 revised full papers presented in this book were carefully reviewed and selected from 31 submissions. The papers focus on the design and analysis of algorithms for online and computationally hard problems.

Randomized Algorithms: Approximation, Generation, and Counting

Russ Bubley
Randomized Algorithms Approximation Generation and Counting Book PDF

Author : Russ Bubley
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781447106951

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Randomized Algorithms: Approximation, Generation, and Counting by Russ Bubley Pdf

Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.

Approximation and Online Algorithms

Evripidis Bampis,Nicole Megow
Approximation and Online Algorithms Book PDF

Author : Evripidis Bampis,Nicole Megow
Publisher : Springer Nature
Page : 253 pages
File Size : 47,5 Mb
Release : 2020-01-24
Category : Mathematics
ISBN : 9783030394790

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Approximation and Online Algorithms by Evripidis Bampis,Nicole Megow Pdf

This book constitutes the thoroughly refereed workshop post-proceedings of the 17th International Workshop on Approximation and Online Algorithms, WAOA 2019, held in Munich, Germany, in September 2019 as part of ALGO 2019. The 16 revised full papers presented together with one invited paper in this book were carefully reviewed and selected from 38 submissions. Topics of interest for WAOA 2018 were: graph algorithms; inapproximability results; network design; packing and covering; paradigms for the design and analysis of approximation and online algorithms; parameterized complexity; scheduling problems; algorithmic game theory; algorithmic trading; coloring and partitioning; competitive analysis; computational advertising; computational finance; cuts and connectivity; geometric problems; mechanism design; resource augmentation; and real-world applications.

Low Rank Approximation

Ivan Markovsky
Low Rank Approximation Book PDF

Author : Ivan Markovsky
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 44,6 Mb
Release : 2011-11-19
Category : Technology & Engineering
ISBN : 9781447122272

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Low Rank Approximation by Ivan Markovsky Pdf

Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation; machine learning for information retrieval and clustering; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; and psychometrics for factor analysis. Software implementation of the methods is given, making the theory directly applicable in practice. All numerical examples are included in demonstration files giving hands-on experience and exercises and MATLAB® examples assist in the assimilation of the theory.

The Design of Approximation Algorithms

David P. Williamson,David B. Shmoys
The Design of Approximation Algorithms Book PDF

Author : David P. Williamson,David B. Shmoys
Publisher : Cambridge University Press
Page : 517 pages
File Size : 40,7 Mb
Release : 2011-04-26
Category : Computers
ISBN : 9781139498173

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The Design of Approximation Algorithms by David P. Williamson,David B. Shmoys Pdf

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.

Approximation Theory and Algorithms for Data Analysis

Armin Iske
Approximation Theory and Algorithms for Data Analysis Book PDF

Author : Armin Iske
Publisher : Springer
Page : 358 pages
File Size : 52,6 Mb
Release : 2018-12-14
Category : Mathematics
ISBN : 9783030052287

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Approximation Theory and Algorithms for Data Analysis by Armin Iske Pdf

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.