JavaScript is disabled for your browser. Some features of this site may not work without it.
Near-Quadratic Bounds for the $L_{1}$ Voronoi Diagram of Moving Points

Author
Chew, L. Paul
Abstract
Given a set of $n$ moving points in the plane, how many topological changes occur in the Voronoi diagram of the points? If each point has constant velocity then there is an upper bound of $O(n^{3})$ [Guibas, Mitchell and Roos] and an easy lower bound of $\Omega(n^{2})$. It is widely believed that the true upper bound should be close to $O(n^{2})$. We show this belief to be true for the case of Voronoi diagrams based on the $L_{1}$ (or $L_{\infty}$) metric; the number of changes is shown to be $O(n^{2} \alpha (n))$ where $\alpha(n)$ grows so slowly it is effectively a small constant for all reasonable values of $n$.
Date Issued
1993-05Publisher
Cornell University
Subject
computer science; technical report
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1348
Type
technical report