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» A quadratic lower bound for colourful simplicial depth
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JCO
2008
153views more  JCO 2008»
13 years 9 months ago
A quadratic lower bound for colourful simplicial depth
We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in Rd is contained in at least (d + 2)2 /4 simplices with one vertex from each set.
Tamon Stephen, Hugh Thomas
DCG
2011
13 years 4 months ago
More Colourful Simplices
We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each ...
Antoine Deza, Tamon Stephen, Feng Xie
COCOON
2007
Springer
14 years 3 months ago
"Resistant" Polynomials and Stronger Lower Bounds for Depth-Three Arithmetical Formulas
We derive quadratic lower bounds on the ∗-complexity of sum-of-products-of-sums (ΣΠΣ) formulas for classes of polynomials f that have too few partial derivatives for the techn...
Maurice J. Jansen, Kenneth W. Regan
COMPGEOM
2004
ACM
14 years 2 months ago
Deterministic sampling and range counting in geometric data streams
We present memory-efficient deterministic algorithms for constructing -nets and -approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic...
Amitabha Bagchi, Amitabh Chaudhary, David Eppstein...