On Central Limit Theorems in Geometrical Probability (Classic Reprint)

Florin Avram, Dimitris Bertsimas

ISBN 10: 1334015201 / ISBN 13: 9781334015205

Published by Forgotten Books, 2024

About this Item

Print on Demand. This book presents a significant development in geometrical probability, proving central limit theorems for three fundamental constructions in computational geometry: the k-nearest graph, the Voronoi diagram, and the Delaunay triangulation. Within this field, the author provides a novel approach using dependency graphs to capture local dependence in these problems. The book establishes that, given a Poisson point process with parameter n, the lengths of these graphs satisfy central limit theorems as n approaches infinity. These results provide a theoretical framework for understanding the asymptotic behavior of these graphs and have implications for designing more efficient algorithms for solving related problems. Additionally, the author explores the relationship between these central limit theorems and efficient algorithms for these problems, demonstrating the potential for faster sequential and parallel algorithms. Overall, this book offers a valuable contribution to geometrical probability and computational geometry, providing new insights into the asymptotic behavior of important combinatorial structures and paving the way for advancements in algorithmic design. 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. Seller Inventory # 9781334015205_0

Bibliographic Details

Title: On Central Limit Theorems in Geometrical ...

Publisher: Forgotten Books

Publication Date: 2024

Binding: Paperback

Condition: New

Book Type: print-on-demand item

About this title

Synopsis:

Excerpt from On Central Limit Theorems in Geometrical Probability

We believe that our results give some partial insight on why a glt might hold for the mst as well. Ramey [10] has attempted to prove a glt for the mst, but his approach, although very interesting, did not succeed since he needed some unproven, but plausible.

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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.