GEOMETRIC DISCREPANCY AN ILLUSTRATED GUIDE ALGORITHMS AND COMBINATORICS

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Geometric Discrepancy

Author : Jiri Matousek
ISBN : 9783642039423
Genre : Mathematics
File Size : 41.79 MB
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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.
Category: Mathematics

Approximation Randomization And Combinatorial Optimization Algorithms And Techniques

Author : Anupam Gupta
ISBN : 9783642325120
Genre : Computers
File Size : 65.11 MB
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This book constitutes the joint refereed proceedings of the 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012, and the 16th International Workshop on Randomization and Computation, RANDOM 2012, held in Cambridge, Massachusetts, USA, in August 2011. The volume contains 28 contributed papers, selected by the APPROX Program Committee out of 70 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 67 submissions. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
Category: Computers

The Discrepancy Method

Author : Bernard Chazelle
ISBN : 0521003571
Genre : Computers
File Size : 79.20 MB
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The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal to students and researchers in computer science, operations research, pure and applied mathematics, and engineering.
Category: Computers

Computational Geometry

Author : Mark de Berg
ISBN : 9783540779735
Genre : Computers
File Size : 79.97 MB
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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.
Category: Computers

Handbook Of Data Structures And Applications Second Edition

Author : Dinesh P. Mehta
ISBN : 9781351645645
Genre : Computers
File Size : 67.50 MB
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The Handbook of Data Structures and Applications was first published over a decade ago. This second edition aims to update the first by focusing on areas of research in data structures that have seen significant progress. While the discipline of data structures has not matured as rapidly as other areas of computer science, the book aims to update those areas that have seen advances. Retaining the seven-part structure of the first edition, the handbook begins with a review of introductory material, followed by a discussion of well-known classes of data structures, Priority Queues, Dictionary Structures, and Multidimensional structures. The editors next analyze miscellaneous data structures, which are well-known structures that elude easy classification. The book then addresses mechanisms and tools that were developed to facilitate the use of data structures in real programs. It concludes with an examination of the applications of data structures. Four new chapters have been added on Bloom Filters, Binary Decision Diagrams, Data Structures for Cheminformatics, and Data Structures for Big Data Stores, and updates have been made to other chapters that appeared in the first edition. The Handbook is invaluable for suggesting new ideas for research in data structures, and for revealing application contexts in which they can be deployed. Practitioners devising algorithms will gain insight into organizing data, allowing them to solve algorithmic problems more efficiently.
Category: Computers

Geometric Approximation Algorithms

Author : Sariel Har-Peled
ISBN : 9780821849118
Genre : Mathematics
File Size : 33.18 MB
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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.
Category: Mathematics

The Algorithm Design Manual

Author : Steven S Skiena
ISBN : 9781848000704
Genre : Computers
File Size : 49.93 MB
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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
Category: Computers

Handbook Of Discrete And Computational Geometry Third Edition

Author : Csaba D. Toth
ISBN : 9781351645911
Genre : Computers
File Size : 32.98 MB
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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 ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly 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 ?eld 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.
Category: Computers

Algorithms In Combinatorial Geometry

Author : Herbert Edelsbrunner
ISBN : 9783642615689
Genre : Computers
File Size : 84.46 MB
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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.
Category: Computers

Understanding Machine Learning

Author : Shai Shalev-Shwartz
ISBN : 9781107057135
Genre : Computers
File Size : 82.49 MB
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Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.
Category: Computers