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COMPGEOM
2005
ACM
14 years 6 days ago
Hadwiger and Helly-type theorems for disjoint unit spheres in R3
Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the ent...
Otfried Cheong, Xavier Goaoc, Andreas Holmsen
CORR
2007
Springer
119views Education» more  CORR 2007»
13 years 10 months ago
Hadwiger and Helly-type theorems for disjoint unit spheres
Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the ent...
Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Syl...
SIAMDM
2010
123views more  SIAMDM 2010»
13 years 8 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...
COMPGEOM
2006
ACM
14 years 4 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
SIGCSE
2005
ACM
180views Education» more  SIGCSE 2005»
14 years 3 months ago
Analyze that: puzzles and analysis of algorithms
The paper advocates a wider use of puzzles and puzzle-like games in teaching the analysis of algorithms. It discusses many specific examples—from classic puzzles of recreational...
Anany Levitin