On the topology of algorithms, I
Journal of Complexity
Fast algorithms for N-dimensional restrictions of hard problems
Journal of the ACM (JACM)
Very fast parallel polynomial arithmetic
SIAM Journal on Computing
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Point location in arrangements of hyperplanes
Information and Computation
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
On decision trees for orthants
Information Processing Letters
Are lower bounds easier over the reals?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
Topological complexity of the range searching
Journal of Complexity
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Boolean Functions: Parallel Computation and Proof Systems
Boolean Functions: Parallel Computation and Proof Systems
VPSPACE and a transfer theorem over the reals
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
VPSPACE and a transfer theorem over the complex field
Theoretical Computer Science
VPSPACE and a transfer theorem over the reals
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Decision versus evaluation in algebraic complexity
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
VPSPACE and a transfer theorem over the complex field
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Dimitri Grigoriev has shown that for any family of N vectors in the d-dimensional linear space E=(F"2)^d, there exists a vector in E which is orthogonal to at least N/3 and at most 2N/3 vectors of the family. We show that the range [N/3,2N/3] can be replaced by the much smaller range [N/2-N/2,N/2+N/2] and we give an efficient, deterministic parallel algorithm which finds a vector achieving this bound. The optimality of the bound is also investigated.