Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Computational geometry: an introduction
Computational geometry: an introduction
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
An optimal algorithm for reporting visible rectangles
Information Processing Letters
Design of Dynamic Data Structures
Design of Dynamic Data Structures
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Dynamic Planar Convex Hull with Optimal Query Time
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Semi-Online Maintenance of Geometric Optima and Measures
SIAM Journal on Computing
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fully Dynamic Orthogonal Range Reporting on RAM
SIAM Journal on Computing
Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Processing a large number of continuous preference top-k queries
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
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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(log1+εn) for an arbitrarily small constant ε0. This improves the previous bound of O(log3/2n). 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(log2 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(nε). As a corollary, we can solve the following problem in O(n1+ε) time: given a triangulated terrain in 3-d of size n, identify all faces that are partially visible from a fixed viewpoint.