An efficient algorithm for the largest empty figure problem based on a 2D cellular automaton architecture

doi:10.1016/S0262-8856(96)01111-0

Image and Vision Computing

Volume 15, Issue 1, January 1997, Pages 35-45

https://doi.org/10.1016/S0262-8856(96)01111-0 Get rights and content

Abstract

An efficient algorithm for determination of the largest empty figure that can be placed between a set of sites on a plane and its VLSI implementation are presented in this paper. The proposed algorithm is based on the Voronoi diagram in the ϱ1 metric which is established through the time evolution of 2-Dimensional Cellular Automata. The proposed algorithm is fast and efficient, and the 2-Dimensional Cellular Automaton architecture presented in this paper achieves a high frequency of operation. A Von-Neumann neighbourhood processor was implemented on a single VLSI chip using a 1.2 μm Double Layer Metal CMOS technology.

References (21)

T. Ohya et al.
A fast Voronoi diagram algorithm with quarternary tree bucketing
Inform. Processing Lett.
(1984)
F. Aurenhammer
Voronoi Diagrams — a survey of a fundamental geometric data structure
ACM Computing Surveys
(1991)
M.I. Shamos et al.
Closest-point problems
L.P. Chew et al.
Voronoi diagrams based on Convex Distance Functions
B. Chazelle et al.
Computing the largest empty rectangle
SIAM J. Comput.
(1986)
A. Aggarwal et al.
Fast algorithms for computing the largest empty rectangle
H. Aonuma et al.
Maximum location of convex objects in a polygon and related dynamic Voronoi diagrams
T. Asano et al.
Computational geometry algorithms
K. Okabe et al.
Spatial Tesselations: Concepts and Applications of Voronoi Diagrams
(1992)
F.P. Preparata et al.
Computational Geometry: An Introduction
(1985)

There are more references available in the full text version of this article.

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An efficient algorithm for the largest empty figure problem based on a 2D cellular automaton architecture

Abstract

Inform. Processing Lett.

Voronoi Diagrams — a survey of a fundamental geometric data structure

ACM Computing Surveys

Closest-point problems

Voronoi diagrams based on Convex Distance Functions

Computing the largest empty rectangle

SIAM J. Comput.

Fast algorithms for computing the largest empty rectangle

Maximum location of convex objects in a polygon and related dynamic Voronoi diagrams

Computational geometry algorithms

Spatial Tesselations: Concepts and Applications of Voronoi Diagrams

Computational Geometry: An Introduction