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ɛ-nets and simplex range queries
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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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Partitioning point sets in 4 dimensions
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Some special vapnik-chervonenkis classes
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Halfplanar range search in linear space and O(n0.695) query time
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On the density of families of sets
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Constructing Belts in Two-Dimensional Arrangements with Applications
inferredcites →https://doi.org/10.1137/1116025openalex-snapshot
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
inferredcites →https://doi.org/10.1145/12130.12158openalex-snapshot
Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension
inferredcites →https://doi.org/10.1145/12130.12173openalex-snapshot
Further applications of random sampling to computational geometry
inferredcites →https://doi.org/10.1145/22145.22163openalex-snapshot
A general approach to d-dimensional geometric queries
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A probabilistic algorithm for the post office problem
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A 3-space partition and its applications
inferredcites →https://doi.org/10.1214/aop/1176995384openalex-snapshot
Central Limit Theorems for Empirical Measures
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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On density of subgraphs of Cartesian products
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Bollobás‐Erdős‐Tuza Conjecture for Graphs With No Induced Ks,t
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Geometric algorithms for the minimum cost assignment problem
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Point Location in Arrangements of Hyperplanes
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Recursion Theoretic Properties of Frequency Computation and Bounded Queries
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Derandomization in Computational Geometry
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On Linear-Time Deterministic Algorithms for Optimization Problems in Fixed Dimension
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Efficient Searching with Linear Constraints
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A Lower Bound for Families of Natarajan Dimension d
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I/O-Efficient Construction of Constrained Delaunay Triangulations
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Exact and Approximation Algorithms for Computing the Dilation Spectrum of Paths, Trees, and Cycles
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A 4-Approximation Algorithm for Guarding 1.5-Dimensional Terrains
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On Exact Learning Halfspaces with Random Consistent Hypothesis Oracle
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Minimizing Interference of a Wireless Ad-Hoc Network in a Plane
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Geometric structures in computational geometry
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Irregularities of Distribution, Derandomization, and Complexity Theory
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Approximation of Multiobjective Optimization Problems
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Property Testing in Computational Geometry
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Approximation Algorithms for k-Line Center
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Recent Developments in the Theory of Arrangements of Surfaces
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On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity and Applications
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Collision avoidance for nonrigid objects
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Towards representation independence in PAC learning
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Learning convex sets under uniform distribution
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Lower bounds on the complexity of simplex range reporting on a pointer machine
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On range searching with semialgebraic sets
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Algorithms for polytope covering and approximation
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ε-approximations of k-label spaces
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Randomized geometric algorithms (abstract)
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Computability of convex sets
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Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications
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VC-dimensions for graphs (extended abstract)
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Sample compression, learnability, and the Vapnik-Chervonenkis dimension
inferred← citeshttps://doi.org/10.1007/3-540-64359-1_714openalex-snapshot
Parallel randomized techniques for some fundamental geometric problems: A survey
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Improved Deterministic Parallel Padded Sorting
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Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles
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Pac Learning, Noise, and Geometry
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Parallel Randomized Techniques for Some Fundamental Geometric Problems
inferred← citeshttps://doi.org/10.1007/978-1-4613-8369-7_3openalex-snapshot
Automatic Mesh Partitioning
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A Remark on Transversal Numbers
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Derandomization in Combinatorial Optimization
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Concentration of Measure for Randomized Algorithms: Techniques and Analysis
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Randomized Algorithms for Geometric Optimization Problems
inferred← citeshttps://doi.org/10.1007/978-1-4615-0755-0_7openalex-snapshot
Gems in the Field of Bounded Queries
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Constant Factor Approximation for Intersecting Line Segments with Disks
inferred← citeshttps://doi.org/10.1007/978-3-030-10564-8_32openalex-snapshot
Capacitated Discrete Unit Disk Cover
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How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths
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On Alternation, VC-dimension and k-fold Union of Sets
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Bounding the Trace Function of a Hypergraph with Applications
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Maximal SRLGs Induced by Disks with Radius r
inferred← citeshttps://doi.org/10.1007/978-3-031-49272-3_12openalex-snapshot
The Complexity of Recognizing Geometric Hypergraphs
inferred← citeshttps://doi.org/10.1007/978-3-031-55598-5_19openalex-snapshot
Guarding Polyominoes Under k-Hop Visibility
inferred← citeshttps://doi.org/10.1007/978-3-032-10503-5_3openalex-snapshot
Approximation in Geometry
inferred← citeshttps://doi.org/10.1007/978-3-319-04696-9_5openalex-snapshot
Multicolor Discrepancy of Arithmetic Structures
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Sketched History: VC Combinatorics, 1826 up to 1975
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Subsampling in Smoothed Range Spaces
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On the Zarankiewicz Problem for Intersection Hypergraphs
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Simplex Range Searching and Its Variants: A Review
inferred← citeshttps://doi.org/10.1007/978-3-319-44479-6_12openalex-snapshot
One-Sided Epsilon-Approximants
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Near-Optimal Lower Bounds for ε-Nets for Half-Spaces and Low Complexity Set Systems
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Teaching and Compressing for Low VC-Dimension
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Using $$\epsilon $$ -nets for Solving the Classification Problem
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Hitting Set Problem for Axis-Parallel Squares Intersecting a Straight Line Is Polynomially Solvable for Any Fixed Range of Square Sizes
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Computing Coverage Kernels Under Restricted Settings
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Approximate Range Searching Using Binary Space Partitions
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Approximately Dominating Representatives
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A Distributed Algorithm to Approximate Node-Weighted Minimum α-Connected (θ,k)-Coverage in Dense Sensor Networks
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Cuttings for Disks and Axis-Aligned Rectangles
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Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
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Efficient Sensor Placement for Surveillance Problems
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ε-Net Approach to Sensor k-Coverage
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Shape Fitting on Point Sets with Probability Distributions
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Polychromatic Coloring for Half-Planes
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Maximum Overlap of Convex Polytopes under Translation
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A Simple Framework for the Generalized Nearest Neighbor Problem
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Partially Specified Nearest Neighbor Search
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Family Complexity and VC-Dimension
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Paul Erdős and Probabilistic Reasoning
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Conflict-Free Coloring and its Applications
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Combinatorics and Algorithms of Arrangements
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Backwards Analysis of Randomized Geometric Algorithms
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Epsilon-Nets and Computational Geometry
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Computational Geometry and its Application to Computer Graphics
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Methoden zur Visualisierung räumlicher geometrischer Daten
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Ray Tracing Algorithms — Theory and Practice
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Durchschnitte, Zerlegungen und Sichtbarkeit
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Aggregate Languages for Constraint Databases
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Geometric Hitting Sets for Disks: Theory and Practice
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An Abstract Approach to Polychromatic Coloring: Shallow Hitting Sets in ABA-free Hypergraphs and Pseudohalfplanes
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Unsplittable Coverings in the Plane
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Learning Conjunctive Concepts in Structural Domains
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Learning nested differences of intersection-closed concept classes
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Sample Compression, Learnability, and the Vapnik-Chervonenkis Dimension
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Discrepancy and approximations for bounded VC-dimension
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Bounding the vertex cover number of a hypergraph
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Efficient ray shooting and hidden surface removal
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A randomized algorithm for fixed-dimensional linear programming
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Optimal randomized parallel algorithms for computational geometry
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Quasi-optimal upper bounds for simplex range searching and new zone theorems
inferred← citeshttps://doi.org/10.1007/bf01928919openalex-snapshot
Collision avoidance for nonrigid objects
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Storing line segments in partition trees
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Randomized geometric algorithms and pseudorandom generators
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Lines in Space: Combinatorics and Algorithms
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Intersection queries in sets of disks
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A deterministic view of random sampling and its use in geometry
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Triangles in space or building (and analyzing) castles in the air
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Applications of random sampling in computational geometry, II
inferred← citeshttps://doi.org/10.1007/bf02187741openalex-snapshot
A fast las vegas algorithm for triangulating a simple polygon
inferred← citeshttps://doi.org/10.1007/bf02187742openalex-snapshot
Implicitly representing arrangements of lines or segments
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Quasi-optimal range searching in spaces of finite VC-dimension
inferred← citeshttps://doi.org/10.1007/bf02187783openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and spheres
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The complexity and construction of many faces in arrangements of lines and of segments
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The complexity of many cells in arrangements of planes and related problems
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Partitioning arrangements of lines I: An efficient deterministic algorithm
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Partitioning arrangements of lines II: Applications
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New applications of random sampling in computational geometry
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Cutting hyperplanes for divide-and-conquer
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Constructing arrangements optimally in parallel
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Dynamic point location in arrangements of hyperplanes
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On counting pairs of intersecting segments and off-line triangle range searching
inferred← citeshttps://doi.org/10.1007/bf02570718openalex-snapshot
Almost optimal set covers in finite VC-dimension
inferred← citeshttps://doi.org/10.1007/bf02573971openalex-snapshot
How hard is half-space range searching?
inferred← citeshttps://doi.org/10.1007/bf02573973openalex-snapshot
Diameter, width, closest line pair, and parametric searching
inferred← citeshttps://doi.org/10.1007/bf02573975openalex-snapshot
On ray shooting in convex polytopes
inferred← citeshttps://doi.org/10.1007/bf02574015openalex-snapshot
On range searching with semialgebraic sets
inferred← citeshttps://doi.org/10.1007/bf02574025openalex-snapshot
Improved bounds on weak ε-nets for convex sets
inferred← citeshttps://doi.org/10.1007/bf02574066openalex-snapshot
Tight upper bounds for the discrepancy of half-spaces
inferred← citeshttps://doi.org/10.1007/bf02574384openalex-snapshot
Almost tight upper bounds for lower envelopes in higher dimensions
inferred← citeshttps://doi.org/10.1007/bf02574389openalex-snapshot
Vapnik-Chervonenkis dimension and (pseudo-)hyperplane arrangements
inferred← citeshttps://doi.org/10.1007/bf02712871openalex-snapshot
Efficient randomized algorithms for some geometric optimization problems
inferred← citeshttps://doi.org/10.1007/bf02716578openalex-snapshot
Vertical decompositions for triangles in 3-space
inferred← citeshttps://doi.org/10.1007/bf02760925openalex-snapshot
Guarding galleries where every point sees a large area
inferred← citeshttps://doi.org/10.1007/bf02897056openalex-snapshot
Guarding galleries where no point sees a small area
inferred← citeshttps://doi.org/10.1007/bfb0022573openalex-snapshot
Recursion theoretic properties of frequency computation and bounded queries (extended abstract)
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Farthest neighbors, maximum spanning trees and related problems in higher dimensions
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Deterministic sampling and optimization
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A singly-exponential stratification scheme for real semi-algebraic varieties and its applications
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Fast range searching with Delaunay Triangulations
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On the number of regular vertices of the union of Jordan regions
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Inclusion-exclusion complexes for pseudodisk collections
inferred← citeshttps://doi.org/10.1007/pl00009309openalex-snapshot
Weak ɛ-Nets for Points on a Hypersphere
inferred← citeshttps://doi.org/10.1007/pl00009325openalex-snapshot
Bounded-Independence Derandomization of Geometric Partitioning with Applications to Parallel Fixed-Dimensional Linear Programming
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On Constants for Cuttings in the Plane
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Trimming of Graphs, with Application to Point Labeling
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Deterministic fault-tolerant connectivity labeling scheme
inferred← citeshttps://doi.org/10.1007/s00453-001-0115-6openalex-snapshot
Optimal Parallel Randomized Algorithms for the Voronoi Diagram of Line Segments in the Plane
inferred← citeshttps://doi.org/10.1007/s00453-004-1107-0openalex-snapshot
Matching Polyhedral Terrains Using Overlays of Envelopes
inferred← citeshttps://doi.org/10.1007/s00453-005-1166-xopenalex-snapshot
Approximation Algorithms for a k-Line Center
inferred← citeshttps://doi.org/10.1007/s00453-011-9517-2openalex-snapshot
Near-Linear Approximation Algorithms for Geometric Hitting Sets
inferred← citeshttps://doi.org/10.1007/s00453-016-0195-yopenalex-snapshot
Convex Hulls Under Uncertainty
inferred← citeshttps://doi.org/10.1007/s00453-016-0246-4openalex-snapshot
Ham-Sandwich Cuts for Abstract Order Types
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An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams
inferred← citeshttps://doi.org/10.1007/s00453-018-0518-2openalex-snapshot
Building an Optimal Point-Location Structure in $$O( sort (n))$$ O ( s o r t ( n ) ) I/Os
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Active-Learning a Convex Body in Low Dimensions
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Small Candidate Set for Translational Pattern Search
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Guarding Polyominoes Under k-Hop Visibility
inferred← citeshttps://doi.org/10.1007/s00454-001-0029-8openalex-snapshot
An Optimal Deterministic Algorithm for Computing the Diameter of a Three-Dimensional Point Set
inferred← citeshttps://doi.org/10.1007/s00454-001-0090-3openalex-snapshot
A Lower Bound for Weak ɛ -Nets in High Dimension
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Bounded VC-Dimension Implies a Fractional Helly Theorem
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Segment Intersection Searching Problems in General Settings
inferred← citeshttps://doi.org/10.1007/s00454-004-1108-4openalex-snapshot
Covering Things with Things
inferred← citeshttps://doi.org/10.1007/s00454-004-1116-4openalex-snapshot
New Constructions of Weak ?-Nets
inferred← citeshttps://doi.org/10.1007/s00454-005-1162-6openalex-snapshot
Conflict-Free Coloring of Points and Simple Regions in the Plane
inferred← citeshttps://doi.org/10.1007/s00454-006-1260-0openalex-snapshot
Covering Planar Graphs with a Fixed Number of Balls
inferred← citeshttps://doi.org/10.1007/s00454-006-1266-7openalex-snapshot
A Two-Dimensional Kinetic Triangulation with Near-Quadratic Topological Changes
inferred← citeshttps://doi.org/10.1007/s00454-006-1273-8openalex-snapshot
Improved Approximation Algorithms for Geometric Set Cover
inferred← citeshttps://doi.org/10.1007/s00454-006-1275-6openalex-snapshot
Multi-Pass Geometric Algorithms
inferred← citeshttps://doi.org/10.1007/s00454-007-9019-9openalex-snapshot
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
inferred← citeshttps://doi.org/10.1007/s00454-008-9116-4openalex-snapshot
Coloring Geometric Range Spaces
inferred← citeshttps://doi.org/10.1007/s00454-008-9118-2openalex-snapshot
On Regular Vertices of the Union of Planar Convex Objects
inferred← citeshttps://doi.org/10.1007/s00454-009-9158-2openalex-snapshot
Cuttings for Disks and Axis-Aligned Rectangles in Three-Space
inferred← citeshttps://doi.org/10.1007/s00454-009-9177-zopenalex-snapshot
On Approximate Range Counting and Depth
inferred← citeshttps://doi.org/10.1007/s00454-009-9201-3openalex-snapshot
Compression Schemes, Stable Definable Families, and o-Minimal Structures
inferred← citeshttps://doi.org/10.1007/s00454-010-9248-1openalex-snapshot
Relative (p,ε)-Approximations in Geometry
inferred← citeshttps://doi.org/10.1007/s00454-010-9285-9openalex-snapshot
Improved Results on Geometric Hitting Set Problems
inferred← citeshttps://doi.org/10.1007/s00454-010-9308-6openalex-snapshot
Range Minima Queries with Respect to a Random Permutation, and Approximate Range Counting
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