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Efficient randomized algorithms for some geometric optimization problems

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What this work says

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

inferredcites →https://doi.org/10.1006/jagm.1994.1038openalex-snapshot
Applications of Parametric Searching in Geometric Optimization
inferredcites →https://doi.org/10.1007/3-540-57155-8_283openalex-snapshot
An optimal algorithm for roundness determination on convex polygons
inferredcites →https://doi.org/10.1007/978-3-642-83539-1_9openalex-snapshot
Davenport-Schinzel Sequences and their Geometric Applications
inferredcites →https://doi.org/10.1007/bf02108667openalex-snapshot
Generalised regression problems in metrology
inferredcites →https://doi.org/10.1007/bf02187740openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1007/bf02187783openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and spheres
inferredcites →https://doi.org/10.1007/bf02187876openalex-snapshot
ɛ-nets and simplex range queries
inferredcites →https://doi.org/10.1007/bf02570705openalex-snapshot
On lazy randomized incremental construction
inferredcites →https://doi.org/10.1007/bf02573973openalex-snapshot
Diameter, width, closest line pair, and parametric searching
inferredcites →https://doi.org/10.1007/bf02574383openalex-snapshot
New bounds for lower envelopes in three dimensions, with applications to visibility in terrains
inferredcites →https://doi.org/10.1007/bf02574384openalex-snapshot
Almost tight upper bounds for lower envelopes in higher dimensions
inferredcites →https://doi.org/10.1007/bfb0035760openalex-snapshot
A singly-exponential stratification scheme for real semi-algebraic varieties and its applications
inferredcites →https://doi.org/10.1016/0020-0190(85)90044-4openalex-snapshot
Constructing the visibility graph for n-line segments in O(n2) time
inferredcites →https://doi.org/10.1016/0020-0190(90)90167-vopenalex-snapshot
Computing the longest diagonal of a simple polygon
inferredcites →https://doi.org/10.1016/0020-0190(91)90177-jopenalex-snapshot
Randomized optimal algorithm for slope selection
inferredcites →https://doi.org/10.1016/0020-0190(93)90234-zopenalex-snapshot
Optimal slope selection via expanders
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/s0747-7171(08)80065-xopenalex-snapshot
An algorithm for generalized point location and its applications
inferredcites →https://doi.org/10.1109/34.6790openalex-snapshot
Computing the width of a set
inferredcites →https://doi.org/10.1109/34.75510openalex-snapshot
Out-of-roundness problem revisited
inferredcites →https://doi.org/10.1137/s0097539792229404openalex-snapshot
On Collision-Free Placements of Simplices and the Closest Pair of Lines in 3-Space
inferredcites →https://doi.org/10.1137/s0097539794265724openalex-snapshot
Computing Envelopes in Four Dimensions with Applications
inferredcites →https://doi.org/10.1142/s0218195992000020openalex-snapshot
A RANDOMIZED ALGORITHM FOR SLOPE SELECTION
inferredcites →https://doi.org/10.1145/160985.161137openalex-snapshot
An expander-based approach to geometric optimization
inferredcites →https://doi.org/10.1145/177424.177427openalex-snapshot
Vertical decompositions for triangles in 3-space
inferredcites →https://doi.org/10.1145/177424.178081openalex-snapshot
Computing envelopes in four dimensions with applications
inferredcites →https://doi.org/10.1145/2157.322410openalex-snapshot
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
inferredcites →https://doi.org/10.1145/220279.220299openalex-snapshot
The overlay of lower envelopes in three dimensions and its applications
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

What points at this work

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

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Incremental and Decremental Maintenance of Planar Width
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Computing the Penetration Depth of Two Convex Polytopes in 3D
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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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Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications
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Randomized Algorithms for Geometric Optimization Problems
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Minimum-Width Double-Slabs and Widest Empty Slabs in High Dimensions
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Computing a Minimum-Width Square Annulus in Arbitrary Orientation
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Circles in the Water: Towards Island Group Labeling
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Minimum-Width Annulus with Outliers: Circular, Square, and Rectangular Cases
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Minimum-Width Square Annulus Intersecting Polygons
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No, Coreset, No Cry
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Geometric Optimization Problems Over Sliding Windows
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Analytical Description of Digital Circles
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Minimum Width Rectangular Annulus
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Computing the Hausdorff Distance of Geometric Patterns and Shapes
inferred← citeshttps://doi.org/10.1007/pl00009392openalex-snapshot
Fitting a Set of Points by a Circle
inferred← citeshttps://doi.org/10.1007/pl00009455openalex-snapshot
Motion Planning for a Convex Polygon in a Polygonal Environment
inferred← citeshttps://doi.org/10.1007/pl00009478openalex-snapshot
Geometric Applications of a Randomized Optimization Technique
inferred← citeshttps://doi.org/10.1007/s00453-005-1166-xopenalex-snapshot
Approximation Algorithms for a k-Line Center
inferred← citeshttps://doi.org/10.1007/s00454-001-0039-6openalex-snapshot
Exact and Approximation Algorithms for Minimum-Width Cylindrical Shells
inferred← citeshttps://doi.org/10.1007/s00454-009-9165-3openalex-snapshot
Dynamic Coresets
inferred← citeshttps://doi.org/10.1007/s00454-022-00433-5openalex-snapshot
Bipartite Diameter and Other Measures Under Translation
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Semi-Algebraic Off-line Range Searching and Biclique Partitions in the Plane
inferred← citeshttps://doi.org/10.1007/s004540010062openalex-snapshot
Approximation Algorithms for Minimum-Width Annuli and Shells
inferred← citeshttps://doi.org/10.1007/s10957-020-01689-8openalex-snapshot
Certified Efficient Global Roundness Evaluation
inferred← citeshttps://doi.org/10.1016/0925-7721(95)00052-6openalex-snapshot
All convex polyhedra can be clamped with parallel jaw grippers
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50003-6openalex-snapshot
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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On the minimum-area rectangular and square annulus problem
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Rearranging a sequence of points onto a line
inferred← citeshttps://doi.org/10.1016/j.comgeo.2025.102173openalex-snapshot
Minimum-width double-slabs and widest empty slabs in high dimensions
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Constrained two-line center problems
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Window queries for intersecting objects, maximal points and approximations using coresets
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Minimum-width annulus with outliers: Circular, square, and rectangular cases
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An optimal algorithm for finding an enclosing planar rectilinear annulus of minimum width
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Computing a minimum-width cubic and hypercubic shell
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An optimal algorithm for the minimum-width cubic shell problem
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Minimum-width rectangular annulus
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Computing a minimum-width square annulus in arbitrary orientation
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Minimum width color spanning annulus
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Minimum-width double-strip and parallelogram annulus
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On k -enclosing slab problems
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Adaptive-randomised self-calibration of electro-mechanical shutters for space imaging
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Approximation algorithms for projective clustering
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Continuous location of dimensional structures
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A (1+ε)-approximation algorithm for 2-line-center
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Offset-polygon annulus placement problems
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Self-calibration of electro-mechanical shutters for space imaging by means of adaptive-randomized techniques
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Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space
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Almost tight upper bounds for vertical decompositions in four dimensions
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Approximate shape fitting via linearization
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Incremental penetration depth estimation between convex polytopes using dual-space expansion
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Bounding Volume Hierarchies of Slab Cut Balls
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Peeling Potatoes Near-Optimally in Near-Linear Time
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Computing Envelopes in Four Dimensions with Applications
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APPROXIMATING THE DIAMETER, WIDTH, SMALLEST ENCLOSING CYLINDER, AND MINIMUM-WIDTH ANNULUS
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COMPUTING ROUNDNESS IS EASY IF THE SET IS ALMOST ROUND
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GEOMETRIC OPTIMIZATION PROBLEMS OVER SLIDING WINDOWS
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Computing the Angularity Tolerance
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ON THE WIDTH AND ROUNDNESS OF A SET OF POINTS IN THE PLANE
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Almost tight upper bounds for vertical decompositions in four dimensions
inferred← citeshttps://doi.org/10.1145/1377676.1377680openalex-snapshot
Dynamic coresets
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Peeling Potatoes Near-Optimally in Near-Linear Time
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Geometric applications of a randomized optimization technique
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Efficient algorithms for geometric optimization
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Computing roundness is easy if the set is almost round
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Approximation and exact algorithms for minimum-width annuli and shells
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Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus
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Computing the width of a three-dimensional point set
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Constrained Two-Line Center Problems
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Time Windowed Data Structures
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On the Minimum-Area Parallelogram Annulus Problem
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The Optimized Iterative Projection Method to Determine the Width of an Arbitrary 3D Object
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Color Spanning Annulus: Square, Rectangle and Equilateral Triangle
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Finding large sticks and potatoes in polygons
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Exact and approximation algorithms for minimum-width cylindrical shells
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Evaluating the cylindricity of a nominally cylindrical point set
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Approximation algorithms for projective clustering
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Penetration depth of two convex polytopes in 3D
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