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Combinatorial Geometry and Its Algorithmic Applications
"Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer ...
The Discrepancy Method
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.
Algorithms and Computation
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.
Data Structures and Efficient Algorithms
Myocarditis and idiopathic dilated cardiomyopathy are being increasingly recognized as important causes of heart disease and heart failure. Immunological mechanisms have long been suspected as playing a role in thesediseases but direct evidence has been lacking. Recently, animal models have be- come available, in which myocarditis can be induced either by infection with cardiotropic viruses or by autoimmuniza- tion with heart-specific antigens. This book presents and analyzes the latest information obtained from experimental models, relating it to the practical problems of diagnosis and treatment of myocarditis.
Algorithms and Computation
This book constitutes the refereed proceedings of the 9th International Symposium on Algorithms and Computation, ISAAC'98, held in Taejon, Korea, in December 1998. The 47 revised full papers presented were carefully reviewed and selected from a total of 102 submissions. The book is divided in topical sections on computational geometry, complexity, graph drawing, online algorithms and scheduling, CAD/CAM and graphics, graph algorithms, randomized algorithms, combinatorial problems, computational biology, approximation algorithms, and parallel and distributed algorithms.
Graph Theory, Combinatorics and Algorithms
Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.
Property Testing
Property Testing is the study of super-fast (randomized) algorithms for approximate decision making. These algorithms are given direct access to items of a huge data set, and determine, whether this data set has some predetermined (global) property or is far from having this property. Remarkably, this approximate decision is made by accessing a small portion of the data set. This state-of-the-art survey presents a collection of extended abstracts and surveys of leading researchers in property testing and related areas; it reflects the program of a mini-workshop on property testing that took place in January 2010 at the Institute for Computer Science (ITCS), Tsinghua University, Beijing, China. The volume contains two editor's introductions, 10 survey papers and 18 extended abstracts.
Algorithms and Data Structures
The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.
Algorithms - ESA 2003
This book constitutes the refereed proceedings of the 11th Annual European Symposium on Algorithms, ESA 2003, held in Budapest, Hungary, in September 2003. The 66 revised full papers presented were carefully reviewed and selected from 165 submissions. The scope of the papers spans the entire range of algorithmics from design and mathematical analysis issues to real-world applications, engineering, and experimental analysis of algorithms.
