Worst-case growth rates of some classical problems of combinatorial optimization
SIAM Journal on Computing
Spacefilling curves and the planar travelling salesman problem
Journal of the ACM (JACM)
Convex hulls of samples from spherically symmetric distributions
Discrete Applied Mathematics
Proceedings of the twelfth annual symposium on Computational geometry
Improved Upper Bounds for Pairing Heaps
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Proximate planar point location
Proceedings of the nineteenth annual symposium on Computational geometry
On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes
Computational Geometry: Theory and Applications
A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces
Discrete & Computational Geometry
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Expected time analysis for Delaunay point location
Computational Geometry: Theory and Applications
Sublinear Geometric Algorithms
SIAM Journal on Computing
On the stabbing number of a random Delaunay triangulation
Computational Geometry: Theory and Applications
A simple entropy-based algorithm for planar point location
ACM Transactions on Algorithms (TALG)
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Complexity of Delaunay triangulation for points on lower-dimensional polyhedra
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for expected-case planar point location
Computational Geometry: Theory and Applications
The Algorithm Design Manual
An experimental study of point location in planar arrangements in CGAL
Journal of Experimental Algorithmics (JEA)
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
A pedagogic JavaScript program for point location strategies
Proceedings of the twenty-seventh annual symposium on Computational geometry
On the asymptotic growth rate of some spanning trees embedded in Rd
Operations Research Letters
Cost of sequential connection for points in space
Operations Research Letters
Adaptive Point Location with almost No Preprocessing in Delaunay Triangulations
ISVD '12 Proceedings of the 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
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We design, analyze, implement, and evaluate a distribution-sensitive point location algorithm based on the classical Jump & Walk, called Keep, Jump, & Walk. For a batch of query points, the main idea is to use previous queries to improve the current one. In practice, Keep, Jump, & Walk is actually a very competitive method to locate points in a triangulation. We also study some constant-memory distribution-sensitive point location algorithms, which work well in practice with the classical space-filling heuristic for fast point location. Regarding point location in a Delaunay triangulation, we show how the Delaunay hierarchy can be used to answer, under some hypotheses, a query q with an O(log#(pq)) randomized expected complexity, where p is a previously located query and #(s) indicates the number of simplices crossed by the line segment s. The Delaunay hierarchy has O(nlogn) time complexity and O(n) memory complexity in the plane, and under certain realistic hypotheses these complexities generalize to any finite dimension. Finally, we combine the good distribution-sensitive behavior of Keep, Jump, & Walk, and the good complexity of the Delaunay hierarchy, into a novel point location algorithm called Keep, Jump, & Climb. To the best of our knowledge, Keep, Jump, & Climb is the first practical distribution-sensitive algorithm that works both in theory and in practice for Delaunay triangulations.