Computational geometry: an introduction
Computational geometry: an introduction
Square Meshes are Not Always Optimal
IEEE Transactions on Computers
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Journal of Parallel and Distributed Computing
Leftmost one computation on meshes with row broadcasting
Information Processing Letters
Convexity problems on meshes with multiple broadcasting
Journal of Parallel and Distributed Computing
Time- and VLSI-optimal convex hull computation on meshes with multiple broadcasting
Information Processing Letters
Time-optimal proximity graph computations on enhanced meshes
Journal of Parallel and Distributed Computing
Array processor with multiple broadcasting
ISCA '85 Proceedings of the 12th annual international symposium on Computer architecture
Location updates for efficient routing in ad hoc networks
Handbook of wireless networks and mobile computing
The Massively Parallel Processor
The Massively Parallel Processor
IEEE Transactions on Parallel and Distributed Systems
Time-Optimal Visibility-Related Algorithms on Meshes with Multiple Broadcasting
IEEE Transactions on Parallel and Distributed Systems
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Voronoi diagram is one of the most fundamental and important geometric data structures. Voronoi diagram was historically defined for a set of points on the plane. The diagram partitions the plane into regions, one per site. The region of a site s consists of all points closer to s than to any other sites on the plane. Concepts of Voronoi diagram are often attributed to Voronoi (J. Reine Angew. Math. 133 (1907) 97) and Dirichlet (J. Reine Angew. Math. 40 (1850) 209). As a result of these early works, often the name Voronoi diagram and Dirichlet tessellation is used. Due to the importance of Voronoi diagrams, it is important that algorithms are devised to compute these structures in an efficient manner. Of course, this will create new opportunities for the applicability of these data structures. Towards this end, this paper presents new results for the computation of Voronoi diagrams for a set of n points, or n disjoint circles on the plane, on a mesh with multiple broadcasting (MMB) of size n × n. The algorithm runs in O(log2 n) time.