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Sinopsis
Excerpt from Parallel Computational Geometry
This paper contributes some parallel algorithms for solving geometric problems (1) Convex hulls in two and three dimensions (2) Voronoi diagrams and proximity problems (3) Detecting segment intersections and triangulating a polygon (4) Polygon optimization problems (5) Creating data structures in two and three dimensions to answer some standard queries.
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Excerpt from Parallel Computational Geometry
This paper contributes some parallel algorithms for solving geometric problems (1) Convex hulls in two and three dimensions (2) Voronoi diagrams and proximity problems (3) Detecting segment intersections and triangulating a polygon (4) Polygon optimization problems (5) Creating data structures in two and three dimensions to answer some standard queries.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from Parallel Computational Geometry
Computational geometry addresses algorithmic problems in diverse areas such as VLSI design, robotics, and computer graphics. Since 1975 there has been a wide development of sequential algorithms for geometric problems, but until 1985 there was little published about developing parallel algorithms for such problems. A notable exception was the Ph.D. research of Anita Chow (1980) which seems to have been the pioneering work in the field but unfortunately only a portion of it has appeared in the open literature.
This paper contributes some parallel algorithms for solving geometric problems:
(1) Convex hulls in two and three dimensions
(2) Voronoi diagrams and proximity problems
(3) Detecting segment intersections and triangulating a polygon
(4) Polygon optimization problems
(5) Creating data structures in two and three dimensions to answer some standard queries.
It is seldom obvious how to generate parallel algorithms in this area since popular techniques such as contour tracing, plane sweeping, or gift wrapping involve an explicitly sequential (iterative) approach (see [Preparata and Shamos (1985)] for more details). In this paper we exploit data-structures that are simple enough to compute efficiently in parallel while being powerful enough to answer queries efficiently. However, the queries may be answered slightly less efficiently than would be possible if the data-structures were constructed sequentially. 'Efficient' here means polylogarithmic in parallel time.
All the algorithms presented here will be NC-algorithms, i.e., algorithms executable in polylog depth on polynomial-size circuits. We caution that the circuits here are slightly different from those used in machine-based complexity theory in that each node of our circuit can compute an infinite precision arithmetic operation. Furthermore these algorithms shall all be described as if they were implemented on a CREW PRAM - a concurrent-read, exclusive-write parallel random access machine. Such a machine is conceived as having a large number of processors with common access to a common memory. Any number of processors can read the same memory cell simultaneously in 0(1) steps, and any processor can write to a memory cell in 0(1) steps, but if two processors attempt to write to the same cell simultaneously then the machine enters an undefined state.
We should mention here that Anita Chow's dissertation pays close attention to the model of computation involved, and in several cases she provides algorithms for implementation on two models of parallel computation: the CREW PRAM model, and the cube-connected cycles (CCC) network. As mentioned before, in the CREW model, all the processors share the same memory; however, in the CCC network, each processor has its own memory, and is connected to at most four other processors. For details on the CCC model, see [Chow (1980)].
It follows from [Kozen and Yap (1985)] that most common computational geometry problems including all the problems considered in this paper have, in principle, NC-algorithms. Recall that they combined the techniques of [Ben-Or, Kozen and Reif (1984)] and [Collins (1975)] to give parallel algorithms for computing cell decompositions with adjacency information; for fixed dimensions, these algorithms are in NC.
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Parallel Computational Geometry Classic Reprint
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Parallel Computational Geometry Classic Reprint
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Parallel Computational Geometry (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book delves into the realm of parallel computational geometry, an advanced field that explores efficient algorithms for solving geometric problems utilizing multiple processors simultaneously. The author, a leading expert in the domain, presents novel algorithms that operate in logarithmic time using a linear number of processors. By exploiting simple yet powerful data structures, the algorithms presented in this book tackle fundamental geometric problems such as constructing convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating polygons, and optimizing circumscribing triangles. These algorithms significantly enhance the efficiency of geometric problem-solving, making them invaluable for researchers and practitioners in computational geometry. The book is meticulously structured to provide a comprehensive understanding of the field. It begins by introducing basic concepts and gradually builds upon them, offering a firm foundation for readers new to parallel computational geometry. The author's clear explanations and illustrative examples make the content accessible to those with varying backgrounds in computer science and mathematics. For seasoned researchers in computational geometry and related fields, this book offers groundbreaking insights into the latest developments and techniques. The author's original contributions expand the boundaries of knowledge in the field, providing valuable resources for ongoing research and practical applications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781330590294_0
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Parallel Computational Geometry (Classic Reprint)
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Forgotten Books, 2015
ISBN 10: 1330590295
ISBN 13: 9781330590294
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Condición: Hervorragend. Zustand: Hervorragend | Seiten: 58 | Sprache: Englisch | Produktart: Bücher. Nº de ref. del artículo: 25798242/1
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