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CORR
2010
Springer
168views Education» more  CORR 2010»
9 years 29 days ago
Bounds on the maximum multiplicity of some common geometric graphs
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in genera...
Adrian Dumitrescu, André Schulz, Adam Sheff...
SIAMDM
2010
123views more  SIAMDM 2010»
9 years 1 months ago
Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons
We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES (k) such that any set S of at least fES (k) points in general posit...
Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Fe...
ORDER
2010
89views more  ORDER 2010»
9 years 2 months ago
On Order Types of Systems of Segments in the Plane
Let r(n) denote the largest integer such that every family C of n pairwise disjoint segments in the plane in general position has r(n) members whose order type can be represented ...
Andrew Suk
COMGEO
2004
ACM
9 years 3 months ago
A lower bound on the number of triangulations of planar point sets
We show that the number of straight-edge triangulations exhibited by any set of n points in general position in the plane is bounded from below by (2.33n). 2004 Elsevier B.V. All ...
Oswin Aichholzer, Ferran Hurtado, Marc Noy
SIGACT
2008
103views more  SIGACT 2008»
9 years 3 months ago
Computational geometry column 50
Two long-open problems have been solved: (1) every sufficiently large planar point set in general position contains the vertices of an empty hexagon; (2) every finite collection o...
Joseph O'Rourke
CORR
2007
Springer
133views Education» more  CORR 2007»
9 years 3 months ago
Space and camera path reconstruction for omni-directional vision
In this paper, we address the inverse problem of reconstructing a scene as well as the camera motion from the image sequence taken by an omni-directional camera. Our structure fro...
Oliver Knill, Jose Ramirez-Herran
IPL
2008
104views more  IPL 2008»
9 years 3 months ago
A note on harmonic subgraphs in labelled geometric graphs
Let S be a set of n points in general position in the plane, labelled bijectively with the integers {0, 1, . . ., n - 1}. Each edge (the straight segment that joins two points) is...
Gabriela Araujo, József Balogh, Ruy Fabila ...
DCG
2006
97views more  DCG 2006»
9 years 3 months ago
k-Sets in Four Dimensions
We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/13...
Jirí Matousek, Micha Sharir, Shakhar Smorod...
DCG
2006
96views more  DCG 2006»
9 years 3 months ago
k-Sets, Convex Quadrilaterals, and the Rectilinear Crossing Number of Kn
We use circular sequences to give an improved lower bound on the minimum number of ( k)
József Balogh, Gelasio Salazar
COMBINATORICS
2006
125views more  COMBINATORICS 2006»
9 years 3 months ago
A Point in Many Triangles
We give a simpler proof of the result of Boros and F
Boris Bukh
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