Geometric Algorithms and Combinatorial Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 364278240X
Total Pages : 374 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Geometric Algorithms and Combinatorial Optimization by : Martin Grötschel

Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.

Geometric Algorithms and Combinatorial Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 3642978819
Total Pages : 374 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Geometric Algorithms and Combinatorial Optimization by : Martin Grötschel

Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.

Geometric Approximation Algorithms

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Publisher : American Mathematical Soc.
ISBN 13 : 0821849115
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Approximation Algorithms by : Sariel Har-Peled

Download or read book Geometric Approximation Algorithms written by Sariel Har-Peled and published by American Mathematical Soc.. This book was released on 2011 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dissertation Abstracts International

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Publisher :
ISBN 13 :
Total Pages : 800 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Dissertation Abstracts International by :

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques

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Publisher : Springer
ISBN 13 : 3540484132
Total Pages : 297 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques by : Dorit Hochbaum

Download or read book Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques written by Dorit Hochbaum and published by Springer. This book was released on 2004-04-22 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM'99, held jointly with the Second International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX'99, in Berkeley, California in August 1999. The volume presents 24 revised full papers selected from 44 submissions and four invited contributions. The papers present a wealth of new results and document the state-of-the-art in the areas covered by the workshop.

Handbook of Graph Theory, Combinatorial Optimization, and Algorithms

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Publisher : CRC Press
ISBN 13 : 1420011073
Total Pages : 1217 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Graph Theory, Combinatorial Optimization, and Algorithms by : Krishnaiyan "KT" Thulasiraman

Download or read book Handbook of Graph Theory, Combinatorial Optimization, and Algorithms written by Krishnaiyan "KT" Thulasiraman and published by CRC Press. This book was released on 2016-01-05 with total page 1217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c

Computational Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 1461210984
Total Pages : 413 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Computational Geometry by : Franco P. Preparata

Download or read book Computational Geometry written by Franco P. Preparata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2

Combinatorial Geometry

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Publisher : John Wiley & Sons
ISBN 13 : 1118031369
Total Pages : 376 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Combinatorial Geometry by : János Pach

Download or read book Combinatorial Geometry written by János Pach and published by John Wiley & Sons. This book was released on 2011-10-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more

A Journey Through Discrete Mathematics

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Publisher : Springer
ISBN 13 : 3319444794
Total Pages : 829 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis A Journey Through Discrete Mathematics by : Martin Loebl

Download or read book A Journey Through Discrete Mathematics written by Martin Loebl and published by Springer. This book was released on 2017-10-11 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Geometry of Cuts and Metrics

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Publisher : Springer
ISBN 13 : 3642042953
Total Pages : 580 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Geometry of Cuts and Metrics by : Michel Marie Deza

Download or read book Geometry of Cuts and Metrics written by Michel Marie Deza and published by Springer. This book was released on 2009-11-12 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.

Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques

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Publisher : Springer
ISBN 13 : 3540318747
Total Pages : 504 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques by : Chandra Chekuri

Download or read book Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques written by Chandra Chekuri and published by Springer. This book was released on 2005-08-25 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2005) and the 9th International Workshop on Randomization and Computation (RANDOM 2005), which took place concurrently at the University of California in Berkeley, on August 22 –24, 2005.

Combinatorial Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 3540292977
Total Pages : 596 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Combinatorial Optimization by : Bernhard Korte

Download or read book Combinatorial Optimization written by Bernhard Korte and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.

Digital and Discrete Geometry

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Publisher : Springer
ISBN 13 : 3319120999
Total Pages : 325 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Digital and Discrete Geometry by : Li M. Chen

Download or read book Digital and Discrete Geometry written by Li M. Chen and published by Springer. This book was released on 2014-12-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData. The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced topics. Chapters especially focus on the applications of these methods to other types of geometry, algebraic topology, image processing, computer vision and computer graphics. Digital and Discrete Geometry: Theory and Algorithms targets researchers and professionals working in digital image processing analysis, medical imaging (such as CT and MRI) and informatics, computer graphics, computer vision, biometrics, and information theory. Advanced-level students in electrical engineering, mathematics, and computer science will also find this book useful as a secondary text book or reference. Praise for this book: This book does present a large collection of important concepts, of mathematical, geometrical, or algorithmical nature, that are frequently used in computer graphics and image processing. These concepts range from graphs through manifolds to homology. Of particular value are the sections dealing with discrete versions of classic continuous notions. The reader finds compact definitions and concise explanations that often appeal to intuition, avoiding finer, but then necessarily more complicated, arguments... As a first introduction, or as a reference for professionals working in computer graphics or image processing, this book should be of considerable value." - Prof. Dr. Rolf Klein, University of Bonn.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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Publisher : Springer Science & Business Media
ISBN 13 : 3540742077
Total Pages : 636 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Moses Charikar

Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Moses Charikar and published by Springer Science & Business Media. This book was released on 2007-08-07 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and the 11th International Workshop on Randomization and Computation, RANDOM 2007, held in Princeton, NJ, USA, in August 2007. The 44 revised full papers presented were carefully reviewed and selected from 99 submissions. Topics of interest covered by the papers 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.

Combinatorial Optimization

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821870662
Total Pages : 464 pages
Book Rating : 4.8/5 (76 download)

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Book Synopsis Combinatorial Optimization by : William Cook

Download or read book Combinatorial Optimization written by William Cook and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a carefully refereed collection of invited survey articles written by outstanding researchers. Aimed at researchers in discrete mathematics, operations research, and the theory of computing, this book offers an in-depth look at many topics not treated in textbooks.

Handbook of Discrete and Computational Geometry

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Publisher : CRC Press
ISBN 13 : 1351645919
Total Pages : 2354 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 2354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Combinatorics, Geometry and Probability

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Publisher : Cambridge University Press
ISBN 13 : 9780521584722
Total Pages : 588 pages
Book Rating : 4.5/5 (847 download)

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Book Synopsis Combinatorics, Geometry and Probability by : Béla Bollobás

Download or read book Combinatorics, Geometry and Probability written by Béla Bollobás and published by Cambridge University Press. This book was released on 1997-05-22 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panorama of combinatorics by the world's experts.