Computational geometry: an introduction
Computational geometry: an introduction
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
An optimal algorithm for constructing oriented Voronoi diagrams and geographic neighborhood graphs
Information Processing Letters
An axiomatic approach to Voronoi-diagrams in 3D
Journal of Computer and System Sciences
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Voronoi Diagrams in the Moscow Metric (Extended Abstract)
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
Abstract Voronoi Diagrams and their Applications
CG '88 Proceedings of the International Workshop on Computational Geometry on Computational Geometry and its Applications
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Computational Geometry on a Systolic Chip
IEEE Transactions on Computers
Parallel computing with generalized cellular automata
Progress in computer research
Parallel computing with generalized cellular automata
Progress in computer research
Experimental Reaction–Diffusion Chemical Processors for Robot Path Planning
Journal of Intelligent and Robotic Systems
Gabriel Graphs in Arbitrary Metric Space and their Cellular Automaton for Many Grids
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
Voronoi-like nondeterministic partition of a lattice by collectives of finite automata
Mathematical and Computer Modelling: An International Journal
Fine-grain discrete Voronoi diagram algorithms in L1 and L∞ norms
Mathematical and Computer Modelling: An International Journal
Multi-robot coverage and exploration on Riemannian manifolds with boundaries
International Journal of Robotics Research
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In this paper, we discuss an automata model for parallel approximation of the discrete Voronoi diagram. Given a subset of the n labeled nodes of two-dimensional lattice of m x m nodes, we wish to construct a Voronoi cell for every given node, i.e., mark such nodes that form Voronoi edges and vertices. Our technique is based on the wave generation in the cellular automata lattice, their spreading and interaction. The waves are generated in such sites that are corresponded to lattice nodes of a given set (which should be separated). In the result of wave interactions a stationary structure is produced-it represents the required elements of the discrete Voronoi diagram. We show how to construct Voronoi-like structure in two-dimensional cellular automata with O(1) and O(n) cell states and 4 (in metric L"1) or 8 (in metric l~) size of cell neighborhood in O(m) time.