Geometry of Cuts and Metrics

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Author: Michel Marie Deza,Monique Laurent

Publisher: Springer

ISBN: 3642042953

Category: Mathematics

Page: 588

View: 6853

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.

Discrete and Computational Geometry

Japanese Conference, JCDCG 2000, Tokyo, Japan, November, 22-25, 2000. Revised Papers

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Author: Jin Akiyama,Mikio Kano,Masatsugu Urabe

Publisher: Springer

ISBN: 3540477381

Category: Computers

Page: 388

View: 9050

Facets of Combinatorial Optimization

Festschrift for Martin Grötschel

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Author: Michael Jünger,Gerhard Reinelt

Publisher: Springer Science & Business Media

ISBN: 3642381898

Category: Mathematics

Page: 506

View: 5843

Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel’s doctoral descendant tree 1983–2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants. This book starts with a personal tribute to Martin Grötschel by the editors (Part I), a contribution by his very special “predecessor” Manfred Padberg on “Facets and Rank of Integer Polyhedra” (Part II), and the doctoral descendant tree 1983–2012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant. The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimization, super classes of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclic graphs and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering. Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, mean-risk optimization and gas network optimization. Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-integer linear optimization for scheduling and routing of fly-in safari planes. The two closing articles are devoted to computational advances in general mixed integer linear optimization, the first by scientists working in industry, the second by scientists working in academia. These articles reflect the “scientific facets” of Martin Grötschel who has set standards in theory, computation and applications.

Geometric Discrepancy

An Illustrated Guide

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Author: Jiri Matousek

Publisher: Springer Science & Business Media

ISBN: 3642039421

Category: Mathematics

Page: 289

View: 1465

What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? This book is an accessible and lively introduction to the area of geometric discrepancy theory, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.

Lectures on Discrete Geometry

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Author: Ji?í Matoušek

Publisher: Springer Science & Business Media

ISBN: 1461300398

Category: Mathematics

Page: 486

View: 7527

The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Handbook of Discrete and Computational Geometry, Second Edition

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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 9781420035315

Category: Mathematics

Page: 1560

View: 4999

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

Spectral Algorithms

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Author: Ravindran Kannan,Santosh Vempala

Publisher: Now Publishers Inc

ISBN: 1601982747

Category: Computers

Page: 139

View: 2322

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the y" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

Algorithms in Combinatorial Geometry

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Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 3642615686

Category: Computers

Page: 423

View: 9873

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

Geometric Approximation Algorithms

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Author: Sariel Har-Peled

Publisher: American Mathematical Soc.

ISBN: 0821849115

Category: Mathematics

Page: 362

View: 6160

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.

Metric Embeddings

Bilipschitz and Coarse Embeddings into Banach Spaces

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Author: Mikhail I. Ostrovskii

Publisher: Walter de Gruyter

ISBN: 3110264013

Category: Mathematics

Page: 384

View: 2367

Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poincaré inequalities, constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees, Banach spaces which do not admit coarse embeddings of expanders, structure of metric spaces which are not coarsely embeddable into a Hilbert space, applications of Markov chains to embeddability problem, metric characterizations of properties of Banach spaces, and Lipschitz free spaces.

Combinatorial Optimization

Theory and Algorithms

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Author: Bernhard Korte,Jens Vygen

Publisher: Springer

ISBN: 3662560399

Category: Mathematics

Page: 698

View: 7013

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial optimization.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

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Author: Bridget S. Webb

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 4259

Computer Vision

Algorithms and Applications

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Author: Richard Szeliski

Publisher: Springer Science & Business Media

ISBN: 9781848829350

Category: Computers

Page: 812

View: 3050

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Integer Programming

State of the Art and Recent Advances

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Integer programming

Page: N.A

View: 7391

DEXA 99

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Author: Antonio Cammelli,A Min Tjoa,Roland R. Wagner

Publisher: IEEE

ISBN: 9780769502816

Category: Computers

Page: 937

View: 1529

Proceedings of the September 1999 workshop on defining requirements for future systems in the areas of database and artificial technologies. The 151 contributions discuss innovative applications and new architectures; mobility in databases and distributed systems; similarity search; web-based inform"

Ars Combinatoria

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 9925