Voronoi Diagrams: Difference between revisions

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[[File:Voronoi Diagrams - Space.png|1000px]]
[[File:Voronoi Diagrams - Space.png|1000px]]


== Pareto Frontier Improvements Graph ==  
== Space-Time Tradeoff Improvements ==  


[[File:Voronoi Diagrams - Pareto Frontier.png|1000px]]
[[File:Voronoi Diagrams - Pareto Frontier.png|1000px]]

Revision as of 15:36, 15 February 2023

Description

Given a set of n points in 2-dimensional space, compute the Voronoi diagram with the n points as seeds.

Parameters

n: number of points

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Fortune's algorithm 1986 $O(nlogn)$ $O(n)$ auxiliary Exact Deterministic Time & Space
Linde–Buzo–Gray algorithm 1980 $O(nlogn)$ Exact Deterministic Time
Bowyer–Watson algorithm 1981 $O(nlogn)$ $O(n)$ auxiliary Exact Deterministic Time

Time Complexity Graph

Voronoi Diagrams - Time.png

Space Complexity Graph

Voronoi Diagrams - Space.png

Space-Time Tradeoff Improvements

Voronoi Diagrams - Pareto Frontier.png