Higher-dimensional voronoi diagrams in linear expected time
TLDR
A general method is presented for determining the mathematical expectation of the combinatorial complexity and other properties of the Voronoi diagram ofn independent and identically distributed points and it is shown that in this case, the complexity of the diagram is ∵(n) for fixedd.Abstract:
A general method is presented for determining the mathematical expectation of the combinatorial complexity and other properties of the Voronoi diagram ofn independent and identically distributed points. The method is applied to derive exact asymptotic bounds on the expected number of vertices of the Voronoi diagram of points chosen from the uniform distribution on the interior of ad-dimensional ball; it is shown that in this case, the complexity of the diagram is ?(n) for fixedd. An algorithm for constructing the Voronoid diagram is presented and analyzed. The algorithm is shown to require only ?(n) time on average for random points from ad-ball assuming a real-RAM model of computation with a constant-time floor function. This algorithm is asymptotically faster than any previously known and optimal in the average-case sense.read more
Citations
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Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
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Three-dimensional alpha shapes
TL;DR: This article introduces the formal notion of the family of α-shapes of a finite point set in R 3 .
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Efficient and Robust Approximate Nearest Neighbor Search Using Hierarchical Navigable Small World Graphs
Yu. A. Malkov,D. A. Yashunin +1 more
TL;DR: Hierarchical Navigable Small World (HNSW) as mentioned in this paper is a fully graph-based approach for approximate K-nearest neighbor search without any need for additional search structures (typically used at the coarse search stage of most proximity graph techniques).
Voronoi diagrams and Delaunay triangulations
TL;DR: The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site as discussed by the authors.
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Randomized incremental construction of Delaunay and Voronoi diagrams
TL;DR: A new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations is given that takes expected timeO(nℝgn) and spaceO( n), and is eminently practical to implement.
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