Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Lectures on Discrete Geometry
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Approximate centerpoints with proofs
Computational Geometry: Theory and Applications
Byzantine vector consensus in complete graphs
Proceedings of the 2013 ACM symposium on Principles of distributed computing
| Hi-index | 0.00 |
Let P be a d-dimensional n-point set. A Tverberg partition of P is a partition of P into r sets P1, ..., Pr such that the convex hulls ch(P1), ..., ch(Pr) have non-empty intersection. A point in the intersection of the convex hulls is called a Tverberg point of depth r for P. A classic result by Tverberg implies that there always exists a Tverberg partition of size n/(d+1), but it is not known how to find such a partition in polynomial time. Therefore, approximate solutions are of interest. We describe a deterministic algorithm that finds a Tverberg partition of size n/4(d+1)3 in time dO(log d) n. This means that for every fixed dimension we can compute an approximate Tverberg point (and hence also an approximate centerpoint) in linear time. Our algorithm is obtained by combining a novel lifting approach with a recent result by Miller and Sheehy.