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Combinatorial complexity bounds for arrangements of curves and spheres
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Research Problems in Discrete Geometry
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Quantifier elimination for real closed fields by cylindrical algebraic decompostion
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Arrangements of curves in the plane — topology, combinatorics, and algorithms
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Algorithms in Combinatorial Geometry
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Davenport-Schinzel Sequences and their Geometric Applications
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A sweepline algorithm for Voronoi diagrams
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Über ein Problem von K. Zarankiewicz
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Beweis einer Vermutung von A. Vázsonyi
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Sphere-and-point incidence relations in high dimensions with applications to unit distances and furthest-neighbor pairs
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Applications of random sampling in computational geometry, II
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Implicitly representing arrangements of lines or segments
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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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New applications of random sampling in computational geometry
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On some problems of elementary and combinatorial geometry
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Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes
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Extremal problems in discrete geometry
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A theorem on arrangements of lines in the plane
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A Problem of Leo Moser About Repeated Distances on the Sphere
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On the Number of Furthest Neighbour Pairs in a Point Set
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Topologically sweeping an arrangement
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Primitives for the manipulation of general subdivisions and the computation of Voronoi
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Primitives for the manipulation of three-dimensional subdivisions
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Triangles in space or building (and analyzing) castles in the Air
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Triangulating a non-convex polytype
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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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Davenport–Schinzel Sequences and Their Geometric Applications**Both authors have been supported by a grant from the U.S.–Israeli Binational Science Foundation. Pankaj Agarwal has also been supported by a National Science Foundation Grant CCR-93–01259, by an Army Research Office MURI grant…
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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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Derandomization in Computational Geometry
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10.1016/b978-044488002-4/50019-1
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The number of unit distances is almost linear for most norms
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A Crossing Lemma for Jordan curves
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Nearly equal distances and Szemerédi's regularity lemma
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Distinct distances between points and lines
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Edge guards for polyhedra in three-space
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A note on visibility-constrained Voronoi diagrams
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Highly incidental patterns on a quadratic hypersurface in R4
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Facility location problems with uncertainty on the plane
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On the diameter of separated point sets with many nearly equal distances
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Extremal problems on triangle areas in two and three dimensions
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On totally positive matrices and geometric incidences
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On the Zarankiewicz problem for intersection hypergraphs
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Improved Elekes-Szabó type estimates using proximity
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Stability versus speed in a computable algebraic model
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Distinct distances in finite planar sets
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Cardinalities of k-distance sets in Minkowski spaces
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Popular distances in 3-space
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Cardinalities of k-distance sets in Minkowski spaces
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On continuum incidence problems related to harmonic analysis
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Faster point set pattern matching in 3-D
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On counting point-hyperplane incidences
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The common exterior of convex polygons in the plane
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Erased arrangements of lines and convex decompositions of polyhedra
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Spheres, molecules, and hidden surface removal
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Extremal Problems Related to the Sylvester—Gallai Theorem
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Partitioning theorems for sets of semi-Pfaffian sets, with applications
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Sphere tangencies, line incidences and Lie’s line-sphere correspondence
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Point–Line Incidences in Space
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Distinct Distances in Three and Higher Dimensions
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On the Number of Tetrahedra with Minimum, Unit, and Distinct Volumes in Three-Space
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Non-Degenerate Spheres in Three Dimensions
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Unit Distances in Three Dimensions
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Counting higher order tangencies for plane curves
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Crossing Numbers and Hard Erdős Problems in Discrete Geometry
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On the Number of Incidences Between Points and Curves
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The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
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Algorithmic semi-algebraic geometry and topology—recent progress and open problems
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Cliques and cycles in distance graphs and graphs of diameters
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A restriction estimate using polynomial partitioning
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Geometric incidence theorems via Fourier analysis
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From harmonic analysis to arithmetic combinatorics
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Distinct distances in the complex plane
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Recent work connected with the Kakeya problem
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A dynamic data structure for flexible molecular maintenance and informatics
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Breaking the 3/2 Barrier for Unit Distances in Three Dimensions
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Relative neighborhood graphs and their relatives
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Incidences between Points and Lines in R^4
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An Improved Bound for Weak Epsilon-Nets in the Plane
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Counting and cutting cycles of lines and rods in space
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Improved algorithms in geometric optimization via expanders
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Randomized multidimensional search trees: further results in dynamic sampling
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Almost tight upper bounds for lower envelopes in higher dimensions
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Improved bounds on planar k-sets and k-levels
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On the complexity of many faces in arrangements of circles
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The number of regular simplices in higher dimensions
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On a Problem Related to Sphere and Circle Packing
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