Robotics Research Technical Report: Computing the Geodesic Center of a Simple Polygon (Classic Reprint) - Softcover

Pollack, R.

9781332115457: Robotics Research Technical Report: Computing the Geodesic Center of a Simple Polygon (Classic Reprint)

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ISBN 10: 1332115454 ISBN 13: 9781332115457

Publisher: Forgotten Books, 2019

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Excerpt from Robotics Research Technical Report: Computing the Geodesic Center of a Simple Polygon

The total time complexity of our algorithm is o(u log2u). The final stage (that of finding the smallest spanning circle of circles), which may be of independent interest in location theory, runs in time o(u log n log log n).

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Publisher: Forgotten Books
Publication date: 2019
Language: English
ISBN 10: 1332115454
ISBN 13: 9781332115457
Binding: Paperback
Number of pages: 31

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Robotics Research Technical Report (Classic Reprint)

R. Pollack, M. Sharir

Published by Forgotten Books, 2018

ISBN 10: 1332115454 ISBN 13: 9781332115457

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Seller: Forgotten Books, London, United Kingdom

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Paperback. Condition: New. Print on Demand. This book introduces an algorithm designed to locate the geodesic center of a simple polygon, which is a point inside the polygon with the minimal maximum distance to any point within the polygon. This geodesic center problem is an expansion of the classic Euclidean facility location problem, where the objective is to find the point that minimizes the distance between the facility and the furthest point in a given set. The algorithm provided by the author calculates the geodesic center of a simple polygon in time O(n log2n), where n is the number of vertices in the polygon. This is an improvement over the existing algorithm by Asano and Toussaint, which achieves O(n4log n) time complexity. The book explores the geometric definitions of geodesic diameter and geodesic center, and explains how to compute the geodesic diameter of a given polygon using a method by Suri. It also discusses topics such as the link diameter and link center, P-convex sets, and shortest path trees within a polygon. The author presents a linear-time technique by Megiddo for linear programming in R2, which is utilized within the algorithm. By decomposing the problem into smaller subproblems and employing fast parallel algorithms, the author achieves efficient sequential optimization. Overall, this book provides a valuable contribution to the field of computational geometry, offering a practical algorithm for a complex problem and advancing the understanding of geodesic center computation. 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. Seller Inventory # 9781332115457_0

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