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Dynamic half-space range reporting and its applications
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Algorithms in Combinatorial Geometry
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Quasi-optimal upper bounds for simplex range searching and new zone theorems
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Applications of a semi-dynamic convex hull algorithm
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Halfspace range search: An algorithmic application ofk-sets
inferredcites →https://doi.org/10.1007/bf02187740openalex-snapshot
Applications of random sampling in computational geometry, II
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An upper bound on the number of planarK-sets
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New applications of random sampling in computational geometry
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Diameter, width, closest line pair, and parametric searching
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Counting triangle crossings and halving planes
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On levels in arrangements and voronoi diagrams
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Euclidean minimum spanning trees and bichromatic closest pairs
inferredcites →https://doi.org/10.1007/bf02574700openalex-snapshot
Points and triangles in the plane and halving planes in space
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The Design of Dynamic Data Structures
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Maintenance of configurations in the plane
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The colored Tverberg's problem and complexes of injective functions
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Decomposable searching problems I. Static-to-dynamic transformation
inferredcites →https://doi.org/10.1016/0925-7721(92)90006-eopenalex-snapshot
Reporting points in halfspaces
inferredcites →https://doi.org/10.1017/s0963548300000225openalex-snapshot
Point Selections and Weak ε-Nets for Convex Hulls
inferredcites →https://doi.org/10.1090/s0894-0347-1989-1001852-0openalex-snapshot
Lower Bounds on the Complexity of Polytope Range Searching
inferredcites →https://doi.org/10.1109/sfcs.1991.185368openalex-snapshot
Randomized multidimensional search trees: lazy balancing and dynamic shuffling
inferredcites →https://doi.org/10.1109/sfcs.1991.185371openalex-snapshot
Randomized multidimensional search trees: further results in dynamic sampling
inferredcites →https://doi.org/10.1109/sfcs.1991.185410openalex-snapshot
Dynamic three-dimensional linear programming
inferredcites →https://doi.org/10.1109/sfcs.1992.267816openalex-snapshot
Dynamic half-space reporting, geometric optimization, and minimum spanning trees
inferredcites →https://doi.org/10.1137/0212052openalex-snapshot
Linear-Time Algorithms for Linear Programming in $R^3 $ and Related Problems
inferredcites →https://doi.org/10.1137/0215019openalex-snapshot
Constructing Belts in Two-Dimensional Arrangements with Applications
inferredcites →https://doi.org/10.1137/0217052openalex-snapshot
A Randomized Algorithm for Closest-Point Queries
inferredcites →https://doi.org/10.1145/100216.100260openalex-snapshot
Solving query-retrieval problems by compacting Voronoi diagrams
inferredcites →https://doi.org/10.1145/103418.103470openalex-snapshot
Approximations and optimal geometric divide-and-conquer
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.2307/2325168openalex-snapshot
Algorithms in Combinatorial Geometry.
inferredcites →https://doi.org/10.5555/320176.320185openalex-snapshot
New techniques for some dynamic closest-point and farthest-point problems
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Deterministic Algorithms for 2-d Convex Programming and 3-d Online Linear Programming
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Incremental and Decremental Maintenance of Planar Width
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Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D
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Facility Location and the Geometric Minimum-Diameter Spanning Tree
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Optimization over k-set Polytopes and Efficient k-set Enumeration
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Dynamic data structures for fat objects and their applications
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Computing the Center of Uncertain Points on Cactus Graphs
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Approximating the k-Level in Three-Dimensional Plane Arrangements
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Spanners for Geometric Intersection Graphs
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An Efficient Algorithm for 2D Euclidean 2-Center with Outliers
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On geometric optimization with few violated constraints
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On ray shooting in convex polytopes
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Output-sensitive results on convex hulls, extreme points, and related problems
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Algorithmic techniques for geometric optimization
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Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions
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The k-Nearest-Neighbor Voronoi Diagram Revisited
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Two Approaches to Building Time-Windowed Geometric Data Structures
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Computing the Minimum Bottleneck Moving Spanning Tree
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Segment Proximity Graphs and Nearest Neighbor Queries amid Disjoint Segments
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A Fully Dynamic Algorithm for Planar Width
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The Projection Median of a Set of Points in ℝ d
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Dynamic Geometric Data Structures via Shallow Cuttings
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Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications
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Eight-Partitioning Points in 3D, and Efficiently Too
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The edge labeling of higher order Voronoi diagrams
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Reporting points in halfspaces
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Arrangements and Their Applications**Work by PA. was supported by Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.–Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR-91-22103 and CCR-93-11127, by…
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Facility location and the geometric minimum-diameter spanning tree
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Triangular range counting query in 2D and its application in finding k nearest neighbors of a line segment
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Polygonal path simplification with angle constraints
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Iterated snap rounding with bounded drift
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Dynamic ham-sandwich cuts in the plane
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Bounded-degree polyhedronization of point sets
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Minimum cuts in geometric intersection graphs
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Dynamic data structures for k-nearest neighbor queries
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On polyhedra induced by point sets in space
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THAAD: Efficient matching queries under temporal abstraction for anomaly detection
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Computing the center of uncertain points on cactus graphs
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Fast Approximation of High-Order Voronoi Diagrams and Distance Transforms on the GPU
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Durable Top-K Instant-Stamped Temporal Records with User-Specified Scoring Functions
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Random sampling, halfspace range reporting, and construction of (≤k)-levels in three dimensions
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Dynamic planar convex hull operations in near-logarithmic amortized time
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A General Technique for Top- $k$ Geometric Intersection Query Problems
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Theoretical and Experimental Analysis of Heuristics for the “Freeze-Tag” Robot Awakening Problem
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Semialgebraic Range Reporting and Emptiness Searching with Applications
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Approximating the k-Level in Three-Dimensional Plane Arrangements
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Finding Relevant Points for Nearest-Neighbor Classification
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Semi-Online Maintenance of Geometric Optima and Measures
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Pseudo-Line Arrangements: Duality, Algorithms, and Applications
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Low-Dimensional Linear Programming with Violations
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Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
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Random Sampling, Halfspace Range Reporting, and Construction of \lowercase$(\le k)$-Levels in Three Dimensions
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REVERSE NEAREST NEIGHBOR QUERIES IN FIXED DIMENSION
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CENTROID TRIANGULATIONS FROM k-SETS
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THREE PROBLEMS ABOUT DYNAMIC CONVEX HULLS
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Iterated snap rounding with bounded drift
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Online geometric reconstruction
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Ray shooting and parametric search
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Ray shooting in convex polytopes
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Minkowski-type theorems and least-squares partitioning
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Algorithms for center and Tverberg points
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A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
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Output-sensitive results on convex hulls, extreme points, and related problems
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Processing a large number of continuous preference top- k queries
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Splitting a complex of convex polytopes in any dimension
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Raising roofs, crashing cycles, and playing pool
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Constructing cuttings in theory and practice
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Efficient algorithms for geometric optimization
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Improved Deterministic Algorithms for Linear Programming in Low Dimensions
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Maintaining the Union of Unit Discs under Insertions with Near-Optimal Overhead
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Dynamic planar convex hull operations in near-logarithmic amortized time
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A fully dynamic algorithm for planar
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Algorithms for center and Tverberg points
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Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications
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The optimal algorithm for dynamic support of the Voronoi Diagram for a set of points
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Approximate Range Counting Revisited
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Spanners for geometric intersection graphs with applications
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Geometric Facility Location Problems on Uncertain Data
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Computing Principal Components Dynamically
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Dynamic Maintenance of Half-Space Depth for Points and Contours
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Output-Sensitive Tools for Range Searching in Higher Dimensions
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Dynamic Maintenance of the Lower Envelope of Pseudo-Lines
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A Unified Framework for Efficiently Processing Ranking Related Queries
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Ray shooting amid balls, farthest point from a line, and range emptiness searching
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A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
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Deterministic algorithms for 2-d convex programming and 3-d online linear programming
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Semi-online maintenance of geometric optima and measures
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