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» A bound on the number of points of a plane curve
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STOC
2002
ACM
99views Algorithms» more  STOC 2002»
14 years 7 months ago
Recognizing string graphs in NP
A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curv...
Marcus Schaefer, Eric Sedgwick, Daniel Stefankovic
JCT
2011
89views more  JCT 2011»
13 years 2 months ago
On lines, joints, and incidences in three dimensions
We extend (and somewhat simplify) the algebraic proof technique of Guth and Katz [7], to obtain several sharp bounds on the number of incidences between lines and points in three ...
György Elekes, Haim Kaplan, Micha Sharir
CCCG
2010
13 years 8 months ago
Some properties of higher order delaunay and gabriel graphs
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the follo...
Prosenjit Bose, Sébastien Collette, Ferran ...
COMPGEOM
1996
ACM
13 years 11 months ago
New Lower Bounds for Convex Hull Problems in Odd Dimensions
We show that in the worst case, (ndd=2e;1 +n logn) sidedness queries are required to determine whether the convex hull of n points in IRd is simplicial, or to determine the number ...
Jeff Erickson
ESA
2009
Springer
127views Algorithms» more  ESA 2009»
14 years 1 months ago
Piercing Translates and Homothets of a Convex Body
According to a classical result of Gr¨unbaum, the transversal number τ(F) of any family F of pairwise-intersecting translates or homothets of a convex body C in Rd is bounded by...
Adrian Dumitrescu, Minghui Jiang