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On k -Hulls and Related Problems

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Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/bf02579338openalex-snapshot
Sorting inc logn parallel steps
inferredcites →https://doi.org/10.1016/0020-0190(85)90080-8openalex-snapshot
A parallel median algorithm
inferredcites →https://doi.org/10.1016/0022-0000(81)90012-xopenalex-snapshot
Maintenance of configurations in the plane
inferredcites →https://doi.org/10.1016/0097-3165(85)90017-2openalex-snapshot
On the number of line separations of a finite set in the plane
inferredcites →https://doi.org/10.1016/0196-6774(85)90011-2openalex-snapshot
Partitioning with two lines in the plane
inferredcites →https://doi.org/10.1016/0304-3975(78)90051-8openalex-snapshot
Finding the intersection of two convex polyhedra
inferredcites →https://doi.org/10.1016/b978-0-7204-2262-7.50018-1openalex-snapshot
Dissection Graphs of Planar Point Sets
inferredcites →https://doi.org/10.1080/00029890.1961.11989615openalex-snapshot
How to Cut A Cake Fairly
inferredcites →https://doi.org/10.1080/00029890.1983.11971254openalex-snapshot
Determining a Fair Border
inferredcites →https://doi.org/10.1109/tc.1978.1675167openalex-snapshot
New Parallel-Sorting Schemes
inferredcites →https://doi.org/10.1137/0204030openalex-snapshot
Parallelism in Comparison Problems
inferredcites →https://doi.org/10.1137/0211012openalex-snapshot
Polygon Retrieval
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/10.1137/0215023openalex-snapshot
Optimal Point Location in a Monotone Subdivision
inferredcites →https://doi.org/10.1145/2157.322410openalex-snapshot
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
inferredcites →https://doi.org/10.1145/7531.7537openalex-snapshot
Slowing down sorting networks to obtain faster sorting algorithms
inferredcites →https://doi.org/10.2307/2974630openalex-snapshot
Algebraic Topology: A First Course.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Data Depth and Maximum Feasible Subsystems
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k-Sets of Convex Inclusion Chains of Planar Point Sets
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Computing a Center-Transversal Line
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Intersecting line segments, ray shooting, and other applications of geometric partitioning techniques
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Optimization in Arrangements
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Epsilon-nets for halfplanes
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Exact parallel algorithms for the location depth and the maximum feasible subsystem problems
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Automatic Mesh Partitioning
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Algorithms for Radon Partitions with Tolerance
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Computational Geometry and Statistical Depth Measures
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Algorithms for computing the center of area of a convex polygon
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The complexity and construction of many faces in arrangements of lines and of segments
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An upper bound on the number of planarK-sets
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On geometric optimization with few violated constraints
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Diameter, width, closest line pair, and parametric searching
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Algorithms for ham-sandwich cuts
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Computing a centerpoint of a finite planar set of points in linear time
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New lower bounds for Hopcroft's problem
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Algorithmic techniques for geometric optimization
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Parametric search and locating supply centers in trees
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Cutting dense point sets in half
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Improved Bounds for Planar k -Sets and Related Problems
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Geometric Lower Bounds for Parametric Matroid Optimization
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Some Combinatorial and Algorithmic Applications of the Borsuk–Ulam Theorem
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Concentration of the empirical level sets of Tukey’s halfspace depth
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Reporting Red--Blue Intersections between Two Sets of Connected Line Segments
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An Improved Bound for k-Sets in Three Dimensions
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Recognition of Flat Orbifolds and the Classification of Tilings in R 3
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The Complexity of Hyperplane Depth in the Plane
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Robust Shape Fitting via Peeling and Grating Coresets
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Geometric medians
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k-Violation linear programming
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Output-sensitive peeling of convex and maximal layers
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Partitioning point sets in arbitrary dimension
inferred← citeshttps://doi.org/10.1016/0925-7721(95)00021-6openalex-snapshot
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…
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50014-0openalex-snapshot
Derandomization in Computational Geometry
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Algorithms for bivariate zonoid depth
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Dynamic ham-sandwich cuts in the plane
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Finding the Θ-guarded region
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Approximate centerpoints with proofs
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Convex hull of points lying on lines in o ( n log n ) time after preprocessing
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Covering a bichromatic point set with two disjoint monochromatic disks
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Point set stratification and Delaunay depth
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Computing the least quartile difference estimator in the plane
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Minimizing the error of linear separators on linearly inseparable data
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Algorithms for Radon partitions with tolerance
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Order-k α-hulls and α-shapes
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Sorting weighted distances with applications to objective function evaluations in single facility location problems
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Improved bounds on planar k-sets and k-levels
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Random sampling, halfspace range reporting, and construction of (≤k)-levels in three dimensions
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An Improved Algorithm for Constructing kth-Order Voronoi Diagrams
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A practical algorithm for weighted k ‐hulls
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Improved Complexity Bounds for Center Location Problems on Networks by Using Dynamic Data Structures
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An Experimental Study of Old and New Depth Measures
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Self-Improving Algorithms for Coordinatewise Maxima and Convex Hulls
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Optimal Algorithms for Geometric Centers and Depth
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Unoriented $Theta$-Maxima in the Plane: Complexity and Algorithms
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Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
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Random Sampling, Halfspace Range Reporting, and Construction of \lowercase$(\le k)$-Levels in Three Dimensions
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Linear optimization queries
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Diameter, width, closest line pair, and parametric searching
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Approximate center points with proofs
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An optimal algorithm for the (≤ k)-levels, with applications to separation and transversal problems
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Geometric partitioning made easier, even in parallel
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Computing a centerpoint of a finite planar set of points in linear time
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Approximating center points with iterated radon points
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Dehn-Sommerville relations, upper bound theorem, and levels in arrangements
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Constructing levels in arrangements and higher order Voronoi diagrams
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Cutting dense point sets in half
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On geometric optimization with few violated constraints
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Shape approximation using k-order alpha-hulls
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Computational geometry
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Geometric range searching
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Convex hull of imprecise points in o(n log n) time after preprocessing
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New lower bounds for Hopcroft's problem
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Geometric lower bounds for parametric matroid optimization
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Efficient algorithms for geometric optimization
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An improved bound for k -sets in three dimensions
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Notes on computing peaks in k-levels and parametric spanning trees
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Applications of random sampling in computational geometry, II
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The complexity of many faces in arrangements of lines of segments
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Algorithms for vertical and orthogonal L1 linear approximation of points
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The second hull of a knotted curve
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On k-sets and applications
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Integer Convex Minimization in Low Dimensions
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The interface between computational and combinatorial geometry
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Robust shape fitting via peeling and grating coresets
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An optimal algorithm for hyperplane depth in the plane
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Approximation algorithms for layered manufacturing
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Fast implementation of depth contours using topological sweep
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Some results in computational and combinatorial geometry
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On computing geometric estimators of location
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