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A singly-exponential stratification scheme for real semi-algebraic varieties and its applications
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Quantifier elimination for real closed fields by cylindrical algebraic decompostion
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Some new effectivity bounds in computational geometry
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Elementary Structure of Real Algebraic Varieties
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Algorithms in Combinatorial Geometry
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Computing in Algebraic Extensions
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Generalized Polynomial Remainder Sequences
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Computing in Algebraic Extensions
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Generalized Polynomial Remainder Sequences
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Some techniques for geometric searching with implicit set representations
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Optimal randomized parallel algorithms for computational geometry
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A deterministic view of random sampling and its use in geometry
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Combinatorial complexity bounds for arrangements of curves and spheres
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Triangulating a nonconvex polytope
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New applications of random sampling in computational geometry
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Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes
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Shape determination for real curves and surfaces
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Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences
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Searching and storing similar lists
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On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
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Some dynamic computational geometry problems
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An algorithm for generalized point location and its applications
inferredcites →https://doi.org/10.1016/s0747-7171(88)80004-xopenalex-snapshot
Real quantifier elimination is doubly exponential
inferredcites →https://doi.org/10.1016/s0747-7171(88)80005-1openalex-snapshot
Solving systems of polynomial inequalities in subexponential time
inferredcites →https://doi.org/10.1016/s0747-7171(88)80008-7openalex-snapshot
Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets
inferredcites →https://doi.org/10.1090/s0002-9939-1964-0161339-9openalex-snapshot
On the Betti Numbers of Real Varieties
inferredcites →https://doi.org/10.1109/sfcs.1985.4openalex-snapshot
Algebraic cell decomposition in NC
inferredcites →https://doi.org/10.1109/sfcs.1987.1openalex-snapshot
A new algebraic method for robot motion planning and real geometry
inferredcites →https://doi.org/10.1109/sfcs.1988.21945openalex-snapshot
A faster PSPACE algorithm for deciding the existential theory of the reals
inferredcites →https://doi.org/10.1109/sfcs.1988.21970openalex-snapshot
A deterministic view of random sampling and its use in geometry
inferredcites →https://doi.org/10.1109/sfcs.1988.21973openalex-snapshot
Combinatorial complexity bounds for arrangements of curves and surfaces
inferredcites →https://doi.org/10.1137/0213031openalex-snapshot
Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm
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Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane
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Optimal Point Location in a Monotone Subdivision
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On Approximations and Incidence in Cylindrical Algebraic Decompositions
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A Randomized Algorithm for Closest-Point Queries
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On Euclid's Algorithm and the Theory of Subresultants
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Planar point location using persistent search trees
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Some algebraic and geometric computations in PSPACE
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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
inferredcites →https://doi.org/10.1145/73393.73432openalex-snapshot
Triangles in space or building (and analyzing) castles in the Air
inferredcites →https://doi.org/10.1145/73833.73876openalex-snapshot
Triangulating a non-convex polytype
inferredcites →https://doi.org/10.1145/800205.806319openalex-snapshot
Polynomial real root isolation by differentiation
inferredcites →https://doi.org/10.1307/mmj/1028999140openalex-snapshot
An inequality for the discriminant of a polynomial.
inferredcites →https://doi.org/10.2307/1969908openalex-snapshot
Elementary Structure of Real Algebraic Varieties
inferredcites →https://doi.org/10.2307/2319112openalex-snapshot
A Comprehensive Introduction to Differential Geometry.
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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Complexity Bounds for Vertical Decompositions of Linear Arrangements in Four Dimensions
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Recent Developments in the Theory of Arrangements of Surfaces
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Computational geometry for the gourmet old fare and new dishes
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Implicit point location in arrangements of line segments, with an application to motion planning
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Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications
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Jack Schwartz and Robotics: The Roaring Eighties
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Decomposition Algorithms in Geometry
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Explainable Reactive Synthesis
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Optimal Point Set Projections onto Regular Grids
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Arrangements in Geometry: Recent Advances and Challenges
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Lines in Space: Combinatorics and Algorithms
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Triangulating a nonconvex polytope
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Applications of a new space-partitioning technique
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inferred← citeshttps://doi.org/10.1007/bf02574015openalex-snapshot
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Almost tight upper bounds for lower envelopes in higher dimensions
inferred← citeshttps://doi.org/10.1007/bf02712871openalex-snapshot
Efficient randomized algorithms for some geometric optimization problems
inferred← citeshttps://doi.org/10.1007/bf02716576openalex-snapshot
The overlay of lower envelopes and its applications
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Vertical decompositions for triangles in 3-space
inferred← citeshttps://doi.org/10.1007/bfb0028246openalex-snapshot
Ray-shooting and isotopy classes of lines in 3-dimensional space
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Vertical Decomposition of a Single Cell in a Three-Dimensional Arrangement of Surfaces
inferred← citeshttps://doi.org/10.1007/pl00009479openalex-snapshot
Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions
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Sharp Bounds for Vertical Decompositions of Linear Arrangements in Four Dimensions
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Segment Intersection Searching Problems in General Settings
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New Constructions of Weak ?-Nets
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Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications
inferred← citeshttps://doi.org/10.1007/s00454-022-00437-1openalex-snapshot
Testing Polynomials for Vanishing on Cartesian Products of Planar Point Sets: Collinearity Testing and Related Problems
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 computation of an arrangement of quadrics in 3D
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Extremal problems on triangle areas in two and three dimensions
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Optimal projections onto grids and finite resolution images
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COMBINATORIAL BOUNDS IN DISTAL STRUCTURES
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On Range Searching with Semialgebraic Sets II
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Treatment planning for a radiosurgical system with general kinematics
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An optimal convex hull algorithm and new results on cuttings
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Almost tight upper bounds for lower envelopes in higher dimensions
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Semialgebraic Range Reporting and Emptiness Searching with Applications
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Almost tight upper bounds for vertical decompositions in four dimensions
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Counting circular arc intersections
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Extremal problems on triangle areas in two and three dimensions
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Incidence and nearest-neighbor problems for lines in 3-space
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Ray shooting in convex polytopes
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New bounds for lower envelopes in three dimensions, with applications to visibility in terrains
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Vertical decompositions for triangles in 3-space
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The overlay of lower envelopes in three dimensions and its applications
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Efficient randomized algorithms for some geometric optimization problems
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Vertical decomposition of a single cell in a three-dimensional arrangement of surfaces and its applications
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Ray shooting amid balls, farthest point from a line, and range emptiness searching
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