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An upper bound on the number of planarK-sets

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What this work says

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

inferredcites →https://doi.org/10.1007/978-3-642-61568-9openalex-snapshot
Algorithms in Combinatorial Geometry
inferredcites →https://doi.org/10.1007/bf02187685openalex-snapshot
Halfspace range search: An algorithmic application ofk-sets
inferredcites →https://doi.org/10.1007/bf02187686openalex-snapshot
More onk-sets of finite sets in the plane
inferredcites →https://doi.org/10.1007/bf02187740openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1007/bf02187879openalex-snapshot
New applications of random sampling in computational geometry
inferredcites →https://doi.org/10.1007/bf02574700openalex-snapshot
Points and triangles in the plane and halving planes in space
inferredcites →https://doi.org/10.1016/0097-3165(84)90081-5openalex-snapshot
On the number of k-subsets of a set of n points 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/10.1016/0097-3165(86)90122-6openalex-snapshot
The number of small semispaces of a finite set of points in the plane
inferredcites →https://doi.org/10.1016/b978-0-7204-2262-7.50018-1openalex-snapshot
Dissection Graphs of Planar Point Sets
inferredcites →https://doi.org/10.1109/sfcs.1989.63458openalex-snapshot
An upper bound on the number of planar k-sets
inferredcites →https://doi.org/10.1137/0216005openalex-snapshot
On k -Hulls and Related Problems
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1145/73833.73849openalex-snapshot
On the number of halving planes
inferredcites →https://doi.org/10.1145/98524.98548openalex-snapshot
Points and triangles in the plane and halving planes in space
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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Bibliography
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Appendix A Summary
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Choosing Subsets with Maximum Weighted Average
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Median problems in location science
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Geometric Set Systems
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Extremal Hypergraphs and Combinatorial Geometry
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Allowable Sequences and Order Types in Discrete and Computational Geometry
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Davenport-Schinzel Sequences and their Geometric Applications
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Rederiving the Upper Bound for Halving Edges Using Cardano’s Formula
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Dynamic half-space range reporting and its applications
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A bound on local minima of arrangements that implies the upper bound theorem
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On the expected number of k-sets
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Algorithms for ham-sandwich cuts
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Points and triangles in the plane and halving planes in space
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Extremal problems for geometric hypergraphs
inferred← citeshttps://doi.org/10.1007/bfb0019430openalex-snapshot
Orders, k-sets and fast halfplane search on paged memory
inferred← citeshttps://doi.org/10.1007/pl00009291openalex-snapshot
Cutting dense point sets in half
inferred← citeshttps://doi.org/10.1007/pl00009348openalex-snapshot
On Levels in Arrangements of Lines, Segments, Planes, and Triangles%
inferred← citeshttps://doi.org/10.1007/pl00009365openalex-snapshot
Extremal Problems for Geometric Hypergraphs
inferred← citeshttps://doi.org/10.1007/pl00009396openalex-snapshot
Geometric Lower Bounds for Parametric Matroid Optimization
inferred← citeshttps://doi.org/10.1007/s00453-002-0999-9openalex-snapshot
A Characterization of Planar Graphs by Pseudo-Line Arrangements
inferred← citeshttps://doi.org/10.1007/s00454-001-0022-2openalex-snapshot
Recognition of Flat Orbifolds and the Classification of Tilings in R 3
inferred← citeshttps://doi.org/10.1007/s00454-002-2840-2openalex-snapshot
On Levels in Arrangements of Curves
inferred← citeshttps://doi.org/10.1007/s00454-005-1165-3openalex-snapshot
On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences
inferred← citeshttps://doi.org/10.1007/s00454-019-00080-3openalex-snapshot
Dense Point Sets with Many Halving Lines
inferred← citeshttps://doi.org/10.1007/s004540010022openalex-snapshot
Point Sets with Many k-Sets
inferred← citeshttps://doi.org/10.1007/s10898-025-01512-6openalex-snapshot
A survey of exact and approximation algorithms for linear-parametric optimization problems
inferred← citeshttps://doi.org/10.1016/0020-0190(94)00134-0openalex-snapshot
k-Violation linear programming
inferred← citeshttps://doi.org/10.1016/0020-0190(94)00201-9openalex-snapshot
A pseudo-algorithmic separation of lines from pseudo-lines
inferred← citeshttps://doi.org/10.1016/b978-0-444-89596-7.50025-0openalex-snapshot
Geometric Algorithms
inferred← citeshttps://doi.org/10.1016/b978-044482537-7/50002-4openalex-snapshot
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…
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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10.1016/b978-044488002-4/50019-1
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Median and center hyperplanes in Minkowski spaces—a unified approach
inferred← citeshttps://doi.org/10.1016/s0012-365x(02)00430-2openalex-snapshot
On halving line arrangements
inferred← citeshttps://doi.org/10.1016/s0166-218x(98)00103-6openalex-snapshot
Median hyperplanes in normed spaces — a survey
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Continuous location of dimensional structures
inferred← citeshttps://doi.org/10.1109/sfcs.2000.892109openalex-snapshot
On levels in arrangements of curves
inferred← citeshttps://doi.org/10.1109/sfcs.2003.1238227openalex-snapshot
On levels in arrangements of curves. II. A simple inequality and its consequences
inferred← citeshttps://doi.org/10.1137/s0097539795281840openalex-snapshot
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
inferred← citeshttps://doi.org/10.1142/s0218195997000314openalex-snapshot
Computational Geometry Column 32
inferred← citeshttps://doi.org/10.1145/1377676.1377691openalex-snapshot
On levels in arrangements of curves, iii
inferred← citeshttps://doi.org/10.1145/160985.161141openalex-snapshot
Dehn-Sommerville relations, upper bound theorem, and levels in arrangements
inferred← citeshttps://doi.org/10.1145/177424.177521openalex-snapshot
Constructing levels in arrangements and higher order Voronoi diagrams
inferred← citeshttps://doi.org/10.1145/177424.177648openalex-snapshot
Cutting dense point sets in half
inferred← citeshttps://doi.org/10.1145/1824777.1824782openalex-snapshot
On the bichromatic k -set problem
inferred← citeshttps://doi.org/10.1145/195058.195110openalex-snapshot
Computational geometry
inferred← citeshttps://doi.org/10.1145/225058.225284openalex-snapshot
Geometric lower bounds for parametric matroid optimization
inferred← citeshttps://doi.org/10.1145/258533.258624openalex-snapshot
Paul Erdös (1913?1996)
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Computational geometry column 32
inferred← citeshttps://doi.org/10.1145/262839.262856openalex-snapshot
On levels in arrangements of lines, segments, planes, and triangles
inferred← citeshttps://doi.org/10.1145/276884.276906openalex-snapshot
Results on k-sets and j-facets via continuous motion
inferred← citeshttps://doi.org/10.1145/276884.276907openalex-snapshot
Point-sets with few k-sets
inferred← citeshttps://doi.org/10.1145/3299869.3300080openalex-snapshot
RRR
inferred← citeshttps://doi.org/10.1145/336154.336171openalex-snapshot
Point sets with many k -sets
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On Finding Rank Regret Representatives
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EXACT ALGORITHMS FOR SIZE CONSTRAINED CLUSTERING
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Depth, crossings and conflicts in discrete geometry
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