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Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas; among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments...

Based on the seminar that took place in Dagstuhl, Germany in June 2011, this contributed volume studies the four important topics within the scientific visualization field: uncertainty visualization, multifield visualization, biomedical visualization and scalable visualization. * Uncertainty visualization deals with uncertain data from simulations or sampled data, uncertainty due to the mathematical processes operating on the data, and uncertainty in the visual representation,* Multifield visual...

This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes cluste...

Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits i...

This text reviews the evolution of the field of visualization, providing innovative examples from various disciplines, highlighting the important role that visualization plays in extracting and organizing the concepts found in complex data. Features: presents a thorough introduction to the discipline of knowledge visualization, its current state of affairs and possible future developments; examines how tables have been used for information visualization in historical textual documents; discusses...

The subject of wavelet analysis has been around for less than 15 years, yet it seems to be popping up everywhere. The major reason for this is its usefulness in applications. Wavelets reduce the data requirements in fields such as signal processing and approximation through their localization property: A function that is zero in an interval has a wavelet expansion whose partial sums are small or even zero. Since most of the information in a signal is in the region where it changes, only the loca...

Image analysis is a computational feat which humans show excellence in, in comp- ison with computers. Yet the list of applications that rely on automatic processing of images has been growing at a fast pace. Biometric authentication by face, ?ngerprint, and iris, online character recognition in cell phones as well as drug design tools are but a few of its benefactors appearing on the headlines. This is, of course, facilitated by the valuable output of the resarch community in the past 30 years....

When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometr...

The only text available on graph theory at the freshman/sophomore level, it covers properties of graphs, presents numerous algorithms, and describes actual applications to chemistry, genetics, music, linguistics, control theory and the social sciences. Illustrated.

Emphasizing graphing technology and business applications, this user-friendly book is the perfect reference for everyday and business mathematics. Solves problems using both algebra and a graphing utility, with the benefits of each illustrated. Uses real data to help readers make connections between the mathematics learned and familiar situations. Uses up-to-date technology including the more powerful features of ZERO(ROOT) and INTERSECT, with minimal use of TRACE. Helps readers quickly identify...

Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations...

Galileo Galilei said he was "reading the book of nature" as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers. Numbers are, after all, a part of nature. As such, looking at and thinking about them is a way of understanding our relationship to nature. But when we do so in a tec...