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COMPGEOM
2004
ACM
14 years 24 days ago
Solution of Scott's problem on the number of directions determined by a point set in 3-space
Let P be a set of n points in Ê3 , not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n − 7 different dir...
János Pach, Rom Pinchasi, Micha Sharir
BILDMED
2004
130views Algorithms» more  BILDMED 2004»
13 years 8 months ago
Prototyping a Planning System for Orbital Reconstruction
In the practice of maxillofacial surgery, one major challenge is the correct reconstruction of malformed or damaged bone structures of the face. Among those, a rather frequent task...
Jan Fischer, Melissa Mekic, Ángel del R&iac...
STOC
2001
ACM
143views Algorithms» more  STOC 2001»
14 years 7 months ago
Computing crossing numbers in quadratic time
We show that for every fixed ? there is a quadratic time algorithm that decides whether a given graph has crossing number at most and, if this is the case, computes a drawing of t...
Martin Grohe
GD
2006
Springer
13 years 11 months ago
The Number of Triangulations on Planar Point Sets
We give a brief account of results concerning the number of triangulations on finite point sets in the plane, both for arbitrary sets and for specific sets such as the n
Emo Welzl
GD
2005
Springer
14 years 26 days ago
Bar k-Visibility Graphs: Bounds on the Number of Edges, Chromatic Number, and Thickness
Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one co...
Alice M. Dean, William Evans, Ellen Gethner, Joshu...