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...
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...
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...
SCALLOP is a highly scalable solver and library for elliptic partial differential equations on regular block-structured domains. SCALLOP avoids high communication overheads algor...
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...