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Almost tight upper bounds for the single cell and zone problems in three dimensions
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/3-540-19488-6_118openalex-snapshot
Arrangements of curves in the plane — topology, combinatorics, and algorithms
inferredcites →https://doi.org/10.1007/978-3-642-61568-9openalex-snapshot
Algorithms in Combinatorial 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/bf02187740openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1007/bf02187744openalex-snapshot
On the general motion-planning problem with two degrees of freedom
inferredcites →https://doi.org/10.1007/bf02189317openalex-snapshot
On the zone of a surface in a hyperplane arrangement
inferredcites →https://doi.org/10.1007/bf02573992openalex-snapshot
On the complexity of a single cell in certain arrangements of surfaces related to motion planning
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/bf02574706openalex-snapshot
Onk-sets in arrangements of curves and surfaces
inferredcites →https://doi.org/10.1007/bf02579170openalex-snapshot
Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes
inferredcites →https://doi.org/10.1016/0097-3165(89)90032-0openalex-snapshot
Sharp upper and lower bounds on the length of general Davenport-Schinzel sequences
inferredcites →https://doi.org/10.1016/0097-3165(94)90027-2openalex-snapshot
On the sum of squares of cell complexities in hyperplane arrangements
inferredcites →https://doi.org/10.1016/s0747-7171(08)80070-3openalex-snapshot
On the two-dimensional davenport-schinzel problem
inferredcites →https://doi.org/10.1109/sfcs.1993.366849openalex-snapshot
Near-quadratic bounds for the motion planning problem for a polygon in a polygonal environment
inferredcites →https://doi.org/10.1112/s0025579300002850openalex-snapshot
The maximum numbers of faces of a convex polytope
inferredcites →https://doi.org/10.1137/0222031openalex-snapshot
On the Zone Theorem for Hyperplane Arrangements
inferredcites →https://doi.org/10.1137/0222077openalex-snapshot
Computing a Face in an Arrangement of Line Segments and Related Problems
inferredcites →https://doi.org/10.1145/177424.177427openalex-snapshot
Vertical decompositions for triangles in 3-space
inferredcites →https://doi.org/10.1145/177424.177445openalex-snapshot
On translational motion planning in 3-space
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
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.
inferred← citeshttps://doi.org/10.1007/3-540-46691-6_1openalex-snapshot
Recent Developments in the Theory of Arrangements of Surfaces
inferred← citeshttps://doi.org/10.1007/3-540-60220-8_55openalex-snapshot
Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications
inferred← citeshttps://doi.org/10.1007/978-1-4471-4282-9openalex-snapshot
From Linear Operators to Computational Biology
inferred← citeshttps://doi.org/10.1007/978-1-4471-4282-9_6openalex-snapshot
Jack Schwartz and Robotics: The Roaring Eighties
inferred← citeshttps://doi.org/10.1007/978-3-540-45058-0_15openalex-snapshot
Hybrid Motion Planning: Coordinating Two Discs Moving among Polygonal Obstacles in the Plane
inferred← citeshttps://doi.org/10.1007/bf01258293openalex-snapshot
Robot motion planning and the single cell problem in arrangements
inferred← citeshttps://doi.org/10.1007/bf02716803openalex-snapshot
A near-quadratic algorithm for planning the motion of a polygon in a polygonal environment
inferred← citeshttps://doi.org/10.1007/pl00009319openalex-snapshot
Vertical Decomposition of a Single Cell in a Three-Dimensional Arrangement of Surfaces
inferred← citeshttps://doi.org/10.1007/s00454-002-2799-zopenalex-snapshot
The Combinatorial and Topological Complexity of a Single Cell
inferred← citeshttps://doi.org/10.1007/s00454-003-2922-9openalex-snapshot
Different Bounds on the Different Betti Numbers of Semi-Algebraic Sets
inferred← citeshttps://doi.org/10.1007/s00454-005-1206-yopenalex-snapshot
Minkowski Sums of Monotone and General Simple Polygons
inferred← citeshttps://doi.org/10.1007/s00454-006-1272-9openalex-snapshot
A Single Cell in an Arrangement of Convex Polyhedra in ${\Bbb R}^3$
inferred← citeshttps://doi.org/10.1007/s00454-010-9312-xopenalex-snapshot
On the Union of Cylinders in Three Dimensions
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…
inferred← citeshttps://doi.org/10.1016/j.ipl.2007.07.010openalex-snapshot
Aspect-ratio Voronoi diagram and its complexity bounds
inferred← citeshttps://doi.org/10.1016/j.jcta.2009.03.008openalex-snapshot
Extremal problems on triangle areas in two and three dimensions
inferred← citeshttps://doi.org/10.1016/s0022-0000(03)00009-6openalex-snapshot
Computing the Betti numbers of arrangements via spectral sequences
inferred← citeshttps://doi.org/10.1016/s0925-7721(97)00030-8openalex-snapshot
Combinatorial complexity of translating a box in polyhedral 3-space
inferred← citeshttps://doi.org/10.1109/focs.2008.25openalex-snapshot
On the Union of Cylinders in Three Dimensions
inferred← citeshttps://doi.org/10.1109/isvd.2006.12openalex-snapshot
Aspect-Ratio Voronoi Diagram with Applications
inferred← citeshttps://doi.org/10.1109/isvd.2006.9openalex-snapshot
Angular Voronoi Diagram with Applications
inferred← citeshttps://doi.org/10.1109/robot.2006.1642164openalex-snapshot
Topology preserving approximation of free configuration space
inferred← citeshttps://doi.org/10.1109/sfcs.1997.646093openalex-snapshot
An improved algorithm for quantifier elimination over real closed fields
inferred← citeshttps://doi.org/10.1109/sfcs.1998.743511openalex-snapshot
On the combinatorial and topological complexity of a single cell
inferred← citeshttps://doi.org/10.1109/sfcs.2002.1181989openalex-snapshot
The partition technique for overlays of envelopes
inferred← citeshttps://doi.org/10.1137/s009753970240700xopenalex-snapshot
The Partition Technique for Overlays of Envelopes
inferred← citeshttps://doi.org/10.1137/s0097539702408387openalex-snapshot
3-Dimensional Euclidean Voronoi Diagrams of Lines with a Fixed Number of Orientations
inferred← citeshttps://doi.org/10.1137/s0097539793250755openalex-snapshot
The Union of Convex Polyhedra in Three Dimensions
inferred← citeshttps://doi.org/10.1142/s0218195998000102openalex-snapshot
Polyhedral Assembly Partitioning Using Maximally Covered Cells in Arrangements of Convex Polytopes
inferred← citeshttps://doi.org/10.1145/1064092.1064099openalex-snapshot
Almost tight bound for a single cell in an arrangement of convex polyhedra in R 3
inferred← citeshttps://doi.org/10.1145/1377676.1377709openalex-snapshot
Extremal problems on triangle areas in two and three dimensions
inferred← citeshttps://doi.org/10.1145/237218.237230openalex-snapshot
Vertical decomposition of a single cell in a three-dimensional arrangement of surfaces and its applications
inferred← citeshttps://doi.org/10.1145/262839.262911openalex-snapshot
On the complexity of the union of fat objects in the plane
inferred← citeshttps://doi.org/10.1145/320211.320240openalex-snapshot
New results on quantifier elimination over real closed fields and applications to constraint databases
inferred← citeshttps://doi.org/10.1145/378583.378705openalex-snapshot
Different bounds on the different Betti numbers of semi-algebraic sets
inferred← citeshttps://doi.org/10.1145/509907.510010openalex-snapshot
Computing the betti numbers of arrangements
inferred← citeshttps://doi.org/10.1145/513400.513427openalex-snapshot
Three dimensional euclidean Voronoi diagrams of lines with a fixed number of orientations
inferred← citeshttps://doi.org/10.5555/1070432.1070452openalex-snapshot
The interface between computational and combinatorial geometry
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