Structures for Algorithms and Applications

Author: Jesus De Loera,Joerg Rambau,Francisco Santos

Publisher: Springer Science & Business Media

ISBN: 9783642129711

Category: Mathematics

Page: 535

View: 9802

Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.
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Author: Gebhard Böckle,Wolfram Decker,Gunter Malle

Publisher: Springer

ISBN: 3319705660

Category: Mathematics

Page: 763

View: 8060

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
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15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013, Proceedings

Author: Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov

Publisher: Springer

ISBN: 3319022970

Category: Computers

Page: 443

View: 9284

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
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Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces

Author: Janine Bennett,Fabien Vivodtzev,Valerio Pascucci

Publisher: Springer

ISBN: 3662449005

Category: Mathematics

Page: 297

View: 478

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.
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Tamari Memorial Festschrift

Author: Folkert Müller-Hoissen,Jean Marcel Pallo,Jim Stasheff

Publisher: Springer Science & Business Media

ISBN: 3034804059

Category: Mathematics

Page: 436

View: 8631

Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations.
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Author: Øyvind Hjelle,Morten Dæhlen

Publisher: Springer Science & Business Media

ISBN: 3540332618

Category: Mathematics

Page: 229

View: 1717

This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.
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Author: Abel Gomes,Irina Voiculescu,Joaquim Jorge,Brian Wyvill,Callum Galbraith

Publisher: Springer Science & Business Media

ISBN: 9781848824065

Category: Computers

Page: 351

View: 9956

Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.
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Author: William Kocay,Donald L. Kreher

Publisher: CRC Press

ISBN: 9780203489055

Category: Mathematics

Page: 504

View: 7240

Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms. Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.
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Algorithms and Applications

Author: Mark de Berg

Publisher: Springer Science & Business Media

ISBN: 3540779736

Category: Computers

Page: 386

View: 5374

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.
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Mathematics, Algorithms and Applications

Author: Kaleem Siddiqi,Stephen Pizer

Publisher: Springer Science & Business Media

ISBN: 140208658X

Category: Mathematics

Page: 439

View: 8454

The last half century has seen the development of many biological or physical t- ories that have explicitly or implicitly involved medial descriptions of objects and other spatial entities in our world. Simultaneously mathematicians have studied the properties of these skeletal descriptions of shape, and, stimulated by the many areas where medial models are useful, computer scientists and engineers have developed numerous algorithms for computing and using these models. We bring this kno- edge and experience together into this book in order to make medial technology more widely understood and used. The book consists of an introductory chapter, two chapters on the major mat- matical results on medial representations, ?ve chapters on algorithms for extracting medial models from boundary or binary image descriptions of objects, and three chapters on applications in image analysis and other areas of study and design. We hope that this book will serve the science and engineering communities using medial models and will provide learning material for students entering this ?eld. We are fortunate to have recruited many of the world leaders in medial theory, algorithms, and applications to write chapters in this book. We thank them for their signi?cant effort in preparing their contributions. We have edited these chapters and have combined them with the ?ve chapters that we have written to produce an integrated whole.
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18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007, Proceedings

Author: Takeshi Tokuyama

Publisher: Springer

ISBN: 3540771204

Category: Computers

Page: 929

View: 7320

This book constitutes the refereed proceedings of the 18th International Symposium on Algorithms and Computation, ISAAC 2007, held in Sendai, Japan, in December 2007. The 77 revised full papers presented together with two invited talks were carefully reviewed and selected from 220 submissions. The papers included topical sections on graph algorithms, computational geometry, complexity, graph drawing, distributed algorithms, optimization, data structure, and game theory.
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A Platform for Combinatorial and Geometric Computing

Author: Kurt Mehlhorn,Stefan Näher

Publisher: Cambridge University Press

ISBN: 9780521563291

Category: Computers

Page: 1018

View: 6650

LEDA is a library of efficient data types and algorithms and a platform for combinatorial and geometric computing on which application programs can be built. In each of the core computer science areas of data structures, graph and network algorithms, and computational geometry, LEDA covers all (and more) that is found in the standard textbooks. LEDA is the first such library; it is written in C++ and is available on many types of machine. Whilst the software is freely available worldwide and is installed at hundreds of sites, this is the first book devoted to the library. Written by the main authors of LEDA, it is the definitive account, describing how the system is constructed and operates and how it can be used. The authors supply ample examples from a range of areas to show how the library can be used in practice, making the book essential for all workers in algorithms, data structures and computational geometry.
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15th International Symposium, ISAAC 2004, Hong Kong, China, December 20-22, 2004, Proceedings

Author: Rudolf Fleischer,Gerhard Trippen

Publisher: Springer Science & Business Media

ISBN: 3540241310

Category: Computers

Page: 935

View: 4469

This book constitutes the refereed proceedings of the 15th International Symposium on Algorithms and Computation, ISAAC 2004, held in Hong Kong, China in December 2004. The 76 revised full papers presented were carefully reviewed and selected from 226 submissions. Among the topics addressed are computational geometry, graph computations, computational combinatorics, combinatorial optimization, computational complexity, scheduling, distributed algorithms, parallel algorithms, data structures, network optimization, randomized algorithms, and computational mathematics more generally.
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Author: Michael Joswig,Thorsten Theobald

Publisher: Springer Science & Business Media

ISBN: 1447148177

Category: Mathematics

Page: 250

View: 5151

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
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Third International Workshop on Randomization and Approximation Techniques in Computer Science, and Second International Workshop on Approximation Algorithms for Combinatorial Optimization Problems RANDOM-APPROX'99,Berkeley, CA, USA, August 8-11, 1999 Pro

Author: Dorit Hochbaum,Klaus Jansen,Jose D.P. Rolim,Alistair Sinclair

Publisher: Springer Science & Business Media

ISBN: 3540663290

Category: Computers

Page: 298

View: 8915

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4th International Workshop, WADS '95, Kingston, Canada, August 16 - 18, 1995. Proceedings

Author: International Workshop on Algorithms and Data Structures,Ont.). WADS '95 (4th : 1995 : Kingston

Publisher: Springer Science & Business Media

ISBN: 9783540602200

Category: Computers

Page: 517

View: 3412

This volume constitutes the proceedings of the Fourth International Workshop on Algorithms and Data Structures, WADS '95, held in Kingston, Canada in August 1995. The book presents 40 full refereed papers selected from a total of 121 submissions together with invited papers by Preparata and Bilardi, Sharir, Toussaint, and Vitanyi and Li. The book addresses various aspects of algorithms, data structures, computational geometry, scheduling, computational graph theory, and searching.
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Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 3642615686

Category: Computers

Page: 423

View: 6463

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.
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International Workshop on Computational Geometry CG '91 Bern, Switzerland, March 21-22, 1991. Proceedings

Author: International Workshop on Computational Geometry,Hanspeter Bieri

Publisher: Springer Science & Business Media

ISBN: 9783540548911

Category: Computers

Page: 320

View: 1016

Radiocarbon After Four Decades: An Interdisciplinary Perspective commemorates the 40th anniversary of radiocarbon dating. The volume presents discussions of every aspect of this dating technique, as well as chronicles of its development and views of future advancements and applications. All of the 64 authors played major roles in establishment, development or application of this revolutionary scientific tool. The 35 chapters provide a solid foundation in the essential topics of radiocarbon dating: Historical Perspectives; The Natural Carbon Cycle; Instrumentation and Sample Preparation; Hydrology; Old World Archaeology; New World Archaeology; Earth Sciences; and Biomedical Applications.
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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 9781420035315

Category: Mathematics

Page: 1560

View: 6602

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
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