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Cutting hyperplanes for divide-and-conquer
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/978-3-319-21852-6_3openalex-snapshot
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
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Algorithms in Combinatorial Geometry
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A deterministic view of random sampling and its use in geometry
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Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1007/bf02187742openalex-snapshot
Implicitly representing arrangements of lines or segments
inferredcites →https://doi.org/10.1007/bf02187805openalex-snapshot
Partitioning arrangements of lines I: An efficient deterministic algorithm
inferredcites →https://doi.org/10.1007/bf02187809openalex-snapshot
Partitioning arrangements of lines II: Applications
inferredcites →https://doi.org/10.1007/bf02187879openalex-snapshot
New applications of random sampling in computational geometry
inferredcites →https://doi.org/10.1007/bf02573985openalex-snapshot
An optimal convex hull algorithm in any fixed dimension
inferredcites →https://doi.org/10.1016/0020-0190(86)90037-2openalex-snapshot
Linear programming in O(n × 3d) time
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Probabilistic construction of deterministic algorithms: Approximating packing integer programs
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A geometric consistency theorem for a symbolic perturbation scheme
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A singly exponential stratification scheme for real semi-algebraic varieties and its applications
inferredcites →https://doi.org/10.1016/0925-7721(94)90009-4openalex-snapshot
Point location among hyperplanes and unidirectional ray-shooting
inferredcites →https://doi.org/10.1109/sfcs.1986.45openalex-snapshot
Probabilistic construction of deterministic algorithms: Approximating packing integer programs
inferredcites →https://doi.org/10.1109/sfcs.1988.21961openalex-snapshot
A Las Vegas algorithm for linear programming when the dimension is small
inferredcites →https://doi.org/10.1137/0213003openalex-snapshot
Linear Time Algorithms for Two- and Three-Variable Linear Programs
inferredcites →https://doi.org/10.1137/0217052openalex-snapshot
A Randomized Algorithm for Closest-Point Queries
inferredcites →https://doi.org/10.1137/1.9781611970074openalex-snapshot
Ten Lectures on the Probabilistic Method
inferredcites →https://doi.org/10.1137/1116025openalex-snapshot
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
inferredcites →https://doi.org/10.1145/103418.103470openalex-snapshot
Approximations and optimal geometric divide-and-conquer
inferredcites →https://doi.org/10.1145/142675.142732openalex-snapshot
Range searching with efficient hierarchical cuttings
inferredcites →https://doi.org/10.1145/2422.322418openalex-snapshot
Linear Programming in Linear Time When the Dimension Is Fixed
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1145/73393.73407openalex-snapshot
A geometric consistency theorem for a symbolic perturbation scheme
inferredcites →https://doi.org/10.1145/77635.77639openalex-snapshot
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
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Linear programming and convex hulls made easy
inferredcites →https://doi.org/10.2307/2325168openalex-snapshot
Algorithms in Combinatorial Geometry.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Derandomization in Computational Geometry
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Selection in Monotone Matrices and Computingkth Nearest Neighbors
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Multi-parameter Minimum Spanning Trees
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Computing a Center-Transversal Line
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Maintenance of a Piercing Set for Intervals with Applications
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Irregularities of Distribution, Derandomization, and Complexity Theory
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Reporting Intersecting Pairs of Polytopes in Two and Three Dimensions
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Computing Homotopic Shortest Paths Efficiently
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Translating a Planar Object to Maximize Point Containment
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Fast separator decomposition for finite element meshes
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Improved Deterministic Parallel Padded Sorting
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Range Closest-Pair Search in Higher Dimensions
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Minimum-Width Double-Slabs and Widest Empty Slabs in High Dimensions
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Simplex Range Searching and Its Variants: A Review
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Approximating the k-Level in Three-Dimensional Plane Arrangements
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An optimal convex hull algorithm in any fixed dimension
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Output-sensitive results on convex hulls, extreme points, and related problems
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Maintenance of a Piercing Set for Intervals with Applications
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Online Point Location in Planar Arrangements and Its Applications
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Computing the Writhing Number of a Polygonal Knot
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Cuttings for Disks and Axis-Aligned Rectangles in Three-Space
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Optimal Deterministic Algorithms for 2-d and 3-d Shallow Cuttings
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Evasive Sets, Covering by Subspaces, and Point-Hyperplane Incidences
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The Geodesic Edge Center of a Simple Polygon
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Semi-Algebraic Off-line Range Searching and Biclique Partitions in the Plane
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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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Derandomization in Computational Geometry
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Approximating the k-Level in Three-Dimensional Plane Arrangements
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Near-Optimal Randomized Algorithms for Selection in Totally Monotone Matrices
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Algorithms for Subpath Convex Hull Queries and Ray-Shooting among Segments
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inferred← citeshttps://doi.org/10.1137/s0097539793244368openalex-snapshot
Ray Shooting Amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions
inferred← citeshttps://doi.org/10.1137/s0097539793256880openalex-snapshot
On Point Location and Motion Planning among Simplices
inferred← citeshttps://doi.org/10.1137/s0097539794268649openalex-snapshot
An Expander-Based Approach to Geometric Optimization
inferred← citeshttps://doi.org/10.1137/s0097539795281840openalex-snapshot
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
inferred← citeshttps://doi.org/10.1137/s0097539796260321openalex-snapshot
Product Range Spaces, Sensitive Sampling, and Derandomization
inferred← citeshttps://doi.org/10.1137/s0097539797325727openalex-snapshot
Fast and Optimal Parallel Multidimensional Search in PRAMs with Applications to Linear Programming and Related Problems
inferred← citeshttps://doi.org/10.1137/s0097539798337212openalex-snapshot
Space-Time Tradeoffs for Emptiness Queries
inferred← citeshttps://doi.org/10.1137/s0097539799350232openalex-snapshot
Constructing Planar Cuttings in Theory and Practice
inferred← citeshttps://doi.org/10.1137/s0895479895284282openalex-snapshot
Fast Nested Dissection for Finite Element Meshes
inferred← citeshttps://doi.org/10.1142/s0218195903001268openalex-snapshot
COMPUTING CLOSEST POINTS FOR SEGMENTS
inferred← citeshttps://doi.org/10.1142/s0218195911003779openalex-snapshot
FINDING SIMPLICES CONTAINING THE ORIGIN IN TWO AND THREE DIMENSIONS
inferred← citeshttps://doi.org/10.1142/s0218195912500069openalex-snapshot
FITTING A STEP FUNCTION TO A POINT SET WITH OUTLIERS BASED ON SIMPLICIAL THICKNESS DATA STRUCTURES
inferred← citeshttps://doi.org/10.1142/s0218195912500100openalex-snapshot
REPORTING BICHROMATIC SEGMENT INTERSECTIONS FROM POINT SETS
inferred← citeshttps://doi.org/10.1142/s0218195913600054openalex-snapshot
IMPROVED POINTER MACHINE AND I/O LOWER BOUNDS FOR SIMPLEX RANGE REPORTING AND RELATED PROBLEMS
inferred← citeshttps://doi.org/10.1145/1032222.1032259openalex-snapshot
Efficient detection of motion patterns in spatio-temporal data sets
inferred← citeshttps://doi.org/10.1145/1137856.1137866openalex-snapshot
Colored intersection searching via sparse rectangular matrix multiplication
inferred← citeshttps://doi.org/10.1145/142675.142732openalex-snapshot
Range searching with efficient hierarchical cuttings
inferred← citeshttps://doi.org/10.1145/142675.142734openalex-snapshot
Ray shooting in convex polytopes
inferred← citeshttps://doi.org/10.1145/167088.167217openalex-snapshot
A deterministic algorithm for the three-dimensional diameter problem
inferred← citeshttps://doi.org/10.1145/177424.177427openalex-snapshot
Vertical decompositions for triangles in 3-space
inferred← citeshttps://doi.org/10.1145/177424.177521openalex-snapshot
Constructing levels in arrangements and higher order Voronoi diagrams
inferred← citeshttps://doi.org/10.1145/177424.178029openalex-snapshot
Almost optimal set covers in finite VC-dimension
inferred← citeshttps://doi.org/10.1145/1810959.1810974openalex-snapshot
The 2-center problem in three dimensions
inferred← citeshttps://doi.org/10.1145/1810959.1811020openalex-snapshot
Computing similarity between piecewise-linear functions
inferred← citeshttps://doi.org/10.1145/195058.195112openalex-snapshot
On point location and motion planning among simplices
inferred← citeshttps://doi.org/10.1145/220279.220281openalex-snapshot
Output-sensitive results on convex hulls, extreme points, and related problems
inferred← citeshttps://doi.org/10.1145/220279.220293openalex-snapshot
New lower bounds for Hopcroft's problem
inferred← citeshttps://doi.org/10.1145/225058.225285openalex-snapshot
Computing faces in segment and simplex arrangements
inferred← citeshttps://doi.org/10.1145/2261250.2261291openalex-snapshot
Self-improving algorithms for coordinate-wise maxima
inferred← citeshttps://doi.org/10.1145/2261250.2261301openalex-snapshot
Improved pointer machine and I/O lower bounds for simplex range reporting and related problems
inferred← citeshttps://doi.org/10.1145/237218.237347openalex-snapshot
On computing Voronoi diagrams by divide-prune-and-conquer
inferred← citeshttps://doi.org/10.1145/237502.237564openalex-snapshot
Parallel multidimensional search using approximation algorithms
inferred← citeshttps://doi.org/10.1145/2582112.2582155openalex-snapshot
The Discrete Fréchet Distance with Shortcuts via Approximate Distance Counting and Selection
inferred← citeshttps://doi.org/10.1145/2582112.2582157openalex-snapshot
Quasi-Polynomial Time Approximation Scheme for Sparse Subsets of Polygons
inferred← citeshttps://doi.org/10.1145/262839.262988openalex-snapshot
Space-time tradeoffs for emptiness queries (extended abstract)
inferred← citeshttps://doi.org/10.1145/262839.263080openalex-snapshot
Time-series similarity problems and well-separated geometric sets
inferred← citeshttps://doi.org/10.1145/2700222openalex-snapshot
The Discrete and Semicontinuous Fréchet Distance with Shortcuts via Approximate Distance Counting and Selection
inferred← citeshttps://doi.org/10.1145/276698.276864openalex-snapshot
Are lower bounds easier over the reals?
inferred← citeshttps://doi.org/10.1145/276884.276915openalex-snapshot
Geometric applications of a randomized optimization technique
inferred← citeshttps://doi.org/10.1145/299917.299918openalex-snapshot
Efficient algorithms for geometric optimization
inferred← citeshttps://doi.org/10.1145/304893.304901openalex-snapshot
Efficient algorithms for maximum regression depth
inferred← citeshttps://doi.org/10.1145/304893.304993openalex-snapshot
On range reporting, ray shooting and k -level construction
inferred← citeshttps://doi.org/10.1145/3326122openalex-snapshot
Approximation Schemes for Independent Set and Sparse Subsets of Polygons
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