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COMPGEOM
2010
ACM
15 years 2 months ago
Lines avoiding balls in three dimensions revisited
Let B be a collection of n arbitrary balls in R3 . We establish an almost-tight upper bound of O(n3+ε ), for any ε > 0, on the complexity of the space F(B) of all the lines t...
Natan Rubin
FOCS
2006
IEEE
15 years 3 months ago
On the Quantum Query Complexity of Local Search in Two and Three Dimensions
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been...
Xiaoming Sun, Andrew Chi-Chih Yao
FOCS
2008
IEEE
15 years 4 months ago
On the Union of Cylinders in Three Dimensions
We show that the combinatorial complexity of the union of n infinite cylinders in R3 , having arbitrary radii, is O(n2+ε ), for any ε > 0; the bound is almost tight in the w...
Esther Ezra
SC
2003
ACM
15 years 2 months ago
SCALLOP: A Highly Scalable Parallel Poisson Solver in Three Dimensions
SCALLOP is a highly scalable solver and library for elliptic partial differential equations on regular block-structured domains. SCALLOP avoids high communication overheads algor...
Gregory T. Balls, Scott B. Baden, Phillip Colella
STOC
2003
ACM
117views Algorithms» more  STOC 2003»
15 years 10 months ago
Distinct distances in three and higher dimensions
Improving an old result of Clarkson et al., we show that the number of distinct distances determined by a set P of n points in three-dimensional space is (n77/141) = (n0.546 ), fo...
Boris Aronov, János Pach, Micha Sharir, G&a...