Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Voronoi diagrams in n · 2o(√lg lg n) time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
In-place 2-d nearest neighbor search
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Distribution-sensitive point location in convex subdivisions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-fourth annual symposium on Computational geometry
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
ACM Transactions on Algorithms (TALG)
Compact oracles for approximate distances around obstacles in the plane
ESA'07 Proceedings of the 15th annual European conference on Algorithms
External memory range reporting on a grid
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Succinct geometric indexes supporting point location queries
ACM Transactions on Algorithms (TALG)
Entropy, triangulation, and point location in planar subdivisions
ACM Transactions on Algorithms (TALG)
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Given n points in the plane with integer coordinates bounded by U \leqslant2^{w}, we show that the Voronoi diagram can be constructed in O(min{n logn/loglogn, n\sqrt {\log U}) expected time by a randomized algorithm on the unit-cost RAM with word size w. Similar results are also obtained for many other fundamental problems in computational geometry, such as constructing the convex hull of a 3-dimensional point set, computing the Euclidean minimum spanning tree of a planar point set, triangulating a polygon with holes, and finding intersections among a set of line segments. These are the first results to beat the \Omega(nlogn) algebraic-decision-tree lower bounds known for these problems. The results are all derived from a new twodimensional version of fusion trees that can answer point location queries in O(min{logn/loglogn, \sqrt {\log U})time with linear space. Higher-dimensional extensions and applications are also mentioned in the paper.