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• W2103189192 abstract "We present three results related to dynamic convex hulls: • A fully dynamic data structure for maintaining a set of n points in the plane so that we can find the edges of the convex hull intersecting a query line, with expected query and amortized update time O( log 1+ε n) for an arbitrarily small constant ε > 0. This improves the previous bound of O( log 3/2 n). • A fully dynamic data structure for maintaining a set of n points in the plane to support halfplane range reporting queries in O( log n+k) time with O( polylog n) expected amortized update time. A similar result holds for 3-dimensional orthogonal range reporting. For 3-dimensional halfspace range reporting, the query time increases to O( log 2 n/ log log n + k). • A semi-online dynamic data structure for maintaining a set of n line segments in the plane, so that we can decide whether a query line segment lies completely above the lower envelope, with query time O( log n) and amortized update time O(n ε ). As a corollary, we can solve the following problem in O(n 1+ε ) time: given a triangulated terrain in 3-d of size n, identify all faces that are partially visible from a fixed viewpoint." @default.
• W2103189192 created "2016-06-24" @default.
• W2103189192 creator A5032955418 @default.
• W2103189192 date "2012-08-01" @default.
• W2103189192 modified "2023-10-18" @default.
• W2103189192 title "THREE PROBLEMS ABOUT DYNAMIC CONVEX HULLS" @default.
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• W2103189192 doi "https://doi.org/10.1142/s0218195912600096" @default.
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