Pollack Sharir (7 results)

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.

Paperback. Condition: New. Print on Demand. This book presents an innovative algorithm to determine whether two disjoint simple polygons can be moved by a sequence of translations to a position sufficiently far from each other without colliding, and if so, produces such a motion. The algorithm can also determine whether a given polygon can be separated from another using a specified number of translations, and if so, produces a motion using the smallest number of translations or a motion with the shortest total translational distance. The problem that this book addresses is a special instance of the motion planning problem that seeks a purely translational collision-free motion of a polygonal object amidst a collection of polygonal obstacles. The author has shown that the existence of a motion of this type can be determined in time that is close to optimal. 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.

Gebunden. Condition: New.

Gebunden. Condition: New.

Hardcover. Condition: Brand New. 1st edition. 853 pages. 9.25x6.25x1.50 inches. In Stock.

Condition: New. Print on Demand pp. 26.

Condition: New. Print on Demand pp. 30.