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COMPGEOM
2006
ACM
15 years 3 months ago
How slow is the k-means method?
The k-means method is an old but popular clustering algorithm known for its observed speed and its simplicity. Until recently, however, no meaningful theoretical bounds were known...
David Arthur, Sergei Vassilvitskii
COMPGEOM
2006
ACM
15 years 3 months ago
An upper bound on the average size of silhouettes
It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides,...
Marc Glisse
COMPGEOM
2006
ACM
15 years 3 months ago
On overlays and minimization diagrams
The overlay of 2 ≤ m ≤ d minimization diagrams of n surfaces in Rd is isomorphic to a substructure of a suitably constructed minimization diagram of mn surfaces in Rd+m−1 . ...
Vladlen Koltun, Micha Sharir
COMPGEOM
2004
ACM
15 years 3 months ago
Extreme elevation on a 2-manifold
Given a smoothly embedded 2-manifold in ¤¦¥ , we define the elevation of a point as the height difference to a canonically defined second point on the same manifold. Our de...
Pankaj K. Agarwal, Herbert Edelsbrunner, John Hare...
COMPGEOM
2004
ACM
15 years 3 months ago
Towards in-place geometric algorithms and data structures
For many geometric problems, there are efficient algorithms that use surprisingly very little extra space other than the given array holding the input. For many geometric query pr...
Hervé Brönnimann, Timothy M. Chan, Eri...