Geometry of Cuts and Metrics

Author: Michel Marie Deza,Monique Laurent

Publisher: Springer

ISBN: 3642042953

Category: Mathematics

Page: 588

View: 815

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

Author: Jin Akiyama,Mikio Kano,Masatsugu Urabe

Publisher: Springer

ISBN: 3540477381

Category: Computers

Page: 388

View: 9919

Facets of Combinatorial Optimization

Festschrift for Martin Grötschel

Author: Michael Jünger,Gerhard Reinelt

Publisher: Springer Science & Business Media

ISBN: 3642381898

Category: Mathematics

Page: 506

View: 3875

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

Author: Jiri Matousek

Publisher: Springer Science & Business Media

ISBN: 3642039421

Category: Mathematics

Page: 289

View: 5404

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.

Discrete and Computational Geometry

Japanese Conference, JCDCG ..., Revised Papers

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Combinatorial geometry

Page: N.A

View: 6468

Combinatorial Optimization

Theory and Algorithms

Author: Bernhard Korte,Jens Vygen

Publisher: Springer

ISBN: 3662560399

Category: Mathematics

Page: 698

View: 4876

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.

Computational Geometry

Algorithms and Applications

Author: Mark de Berg

Publisher: Springer Science & Business Media

ISBN: 3540779736

Category: Computers

Page: 386

View: 5440

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Bridget S. Webb

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 3147

Applications of stress theory

realizing graphs and kneser-poulsen

Author: Teresa Maria Belk

Publisher: N.A

ISBN: N.A

Category:

Page: 166

View: 5618

Integer Programming

State of the Art and Recent Advances

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Integer programming

Page: N.A

View: 8123

DEXA 99

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

Publisher: IEEE

ISBN: 9780769502816

Category: Computers

Page: 937

View: 5088

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"

Algorithms in Combinatorial Geometry

Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 3642615686

Category: Computers

Page: 423

View: 4835

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.

Spectral Algorithms

Author: Ravindran Kannan,Santosh Vempala

Publisher: Now Publishers Inc

ISBN: 1601982747

Category: Computers

Page: 139

View: 7129

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.

Revue de mathématique élémentaires

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7161

Elemente der Mathematik (EL) publishes survey articles about important developments in the field of mathematics; stimulating shorter communications that tackle more specialized questions; and papers that report on the latest advances in mathematics and applications in other disciplines. The journal does not focus on basic research. Rather, its articles seek to convey to a wide circle of readers - teachers, students, engineers, professionals in industry and administration - the relevance, intellectual challenge and vitality of mathematics today. The Problems Section, covering a diverse range of exercises of varying degrees of difficulty, encourages an active grappling with mathematical problems.

Ars Combinatoria

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 8829

Geometric Approximation Algorithms

Author: Sariel Har-Peled

Publisher: American Mathematical Soc.

ISBN: 0821849115

Category: Mathematics

Page: 362

View: 9117

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.

The Design of Approximation Algorithms

Author: David P. Williamson,David B. Shmoys

Publisher: Cambridge University Press

ISBN: 1139498177

Category: Computers

Page: N.A

View: 3321

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.

Handbook of Discrete and Computational Geometry, Second Edition

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

Publisher: CRC Press

ISBN: 9781420035315

Category: Mathematics

Page: 1560

View: 3123

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