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Quasi-optimal upper bounds for simplex range searching and new zone theorems
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/978-3-642-61568-9openalex-snapshot
Algorithms in Combinatorial Geometry
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Data Structures and Algorithms 3
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A deterministic view of random sampling and its use in geometry
inferredcites →https://doi.org/10.1007/bf02123007openalex-snapshot
Triangles in space or building (and analyzing) castles in the air
inferredcites →https://doi.org/10.1007/bf02187732openalex-snapshot
The upper envelope of piecewise linear functions and the boundary of a region enclosed by convex plates: Combinatorial analysis
inferredcites →https://doi.org/10.1007/bf02187733openalex-snapshot
The upper envelope of piecewise linear functions: Algorithms and applications
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The upper envelope of piecewise linear functions: Tight bounds on the number of faces
inferredcites →https://doi.org/10.1007/bf02187740openalex-snapshot
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/bf02187743openalex-snapshot
Quasi-optimal range searching in spaces of finite VC-dimension
inferredcites →https://doi.org/10.1007/bf02187783openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and spheres
inferredcites →https://doi.org/10.1007/bf02187784openalex-snapshot
The complexity and construction of many faces in arrangements of lines and of segments
inferredcites →https://doi.org/10.1007/bf02187807openalex-snapshot
Triangulating a nonconvex polytope
inferredcites →https://doi.org/10.1007/bf02187809openalex-snapshot
Partitioning arrangements of lines II: Applications
inferredcites →https://doi.org/10.1007/bf02187878openalex-snapshot
Computing convolutions by reciprocal search
inferredcites →https://doi.org/10.1007/bf02187879openalex-snapshot
New applications of random sampling in computational geometry
inferredcites →https://doi.org/10.1007/bf02187902openalex-snapshot
Separating two simple polygons by a sequence of translations
inferredcites →https://doi.org/10.1016/0020-0190(86)90088-8openalex-snapshot
Halfplanar range search in linear space and O(n0.695) query time
inferredcites →https://doi.org/10.1016/0196-6774(86)90004-0openalex-snapshot
Searching and storing similar lists
inferredcites →https://doi.org/10.1016/0196-6774(86)90033-7openalex-snapshot
Point retrieval for polygons
inferredcites →https://doi.org/10.1016/0304-3975(91)90261-yopenalex-snapshot
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
inferredcites →https://doi.org/10.1016/s0019-9958(84)80040-6openalex-snapshot
Geometric retrieval problems
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/10.1137/0217052openalex-snapshot
A Randomized Algorithm for Closest-Point Queries
inferredcites →https://doi.org/10.1145/103418.103470openalex-snapshot
Approximations and optimal geometric divide-and-conquer
inferredcites →https://doi.org/10.1145/22145.22163openalex-snapshot
A general approach to d-dimensional geometric queries
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1145/73393.73400openalex-snapshot
Implicitly representing arrangements of lines or segments
inferredcites →https://doi.org/10.1145/73833.73876openalex-snapshot
Triangulating a non-convex polytype
inferredcites →https://doi.org/10.1145/800061.808755openalex-snapshot
A 3-space partition and its applications
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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Selection in Monotone Matrices and Computingkth Nearest Neighbors
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Range Searching and Point Location among Fat Objects
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Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D
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Geometric Shortest Paths in the Plane
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Straight-Path Queries in Trajectory Data
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Simplex Range Searching and Its Variants: A Review
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Efficient View Point Selection for Silhouettes of Convex Polyhedra
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Weak Visibility of Two Objects in Planar Polygonal Scenes
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Relative Convex Hulls in Semi-dynamic Subdivisions
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Improved Algorithms for the Point-Set Embeddability Problem for Plane 3-Trees
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Embedding Plane 3-Trees in ℝ2 and ℝ3
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Geometric Shortest Paths in the Plane
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Epsilon-Nets and Computational Geometry
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Dynamic half-space range reporting and its applications
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How hard is half-space range searching?
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Range searching with efficient hierarchical cuttings
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New lower bounds for Hopcroft's problem
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Range searching and point location among fat objects
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Motion Planning for a Convex Polygon in a Polygonal Environment
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Determining the Castability of Simple Polyhedra
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Relative Convex Hulls in Semi-Dynamic Arrangements
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Segment Intersection Searching Problems in General Settings
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Tight Lower Bounds for Halfspace Range Searching
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Computing Shapley Values in the Plane
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Simplex range reporting on a pointer machine
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Computing depth orders for fat objects and related problems
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Point location in zones of k-flats in arrangements
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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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Planar point sets determine many pairwise crossing segments
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Querying simplexes in quasi-triangulation
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Weak visibility counting in simple polygons
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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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Ray shooting and stone throwing with near-linear storage
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Efficient view point selection for silhouettes of convex polyhedra
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Chromatic distribution of k-nearest neighbors of a line segment in a planar colored point set
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Straight-path queries in trajectory data
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Efficient algorithms for counting and reporting pairwise intersections between convex polygons
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Computing homotopic shortest paths in the plane
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3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects
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Geometric range searching and its relatives
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An Optimal Lower Bound for Simplex Range Reporting
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Shooting Permanent Rays among Disjoint Polygons in the Plane
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Plane 3-Trees: Embeddability and Approximation
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Ray Shooting Amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions
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Ray Shooting Amidst Spheres in Three Dimensions and Related Problems
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Surface Approximation and Geometric Partitions
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Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
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ON ENUMERATING AND SELECTING DISTANCES
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IMPROVED POINTER MACHINE AND I/O LOWER BOUNDS FOR SIMPLEX RANGE REPORTING AND RELATED PROBLEMS
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IMPROVED ALGORITHMS FOR THE POINT-SET EMBEDDABILITY PROBLEM FOR PLANE 3-TREES
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Range searching with efficient hierarchical cuttings
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Ray shooting in convex polytopes
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Tight lower bounds for halfspace range searching
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Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications
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New lower bounds for Hopcroft's problem
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Improved pointer machine and I/O lower bounds for simplex range reporting and related problems
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Efficient perspective-accurate silhouette computation and applications
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Segment intersection searching problems in general settings
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Approximating the Simplicial Depth
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An efficient algorithm for terrain simplification
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Surface approximation and geometric partitions
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Output-sensitive construction of the union of triangles
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