eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-31
51:1
51:15
10.4230/LIPIcs.ESA.2021.51
article
Improved Approximation Algorithms for Tverberg Partitions
Har-Peled, Sariel
1
https://orcid.org/0000-0003-2638-9635
Zhou, Timothy
1
Department of Computer Science, University of Illinois, Urbana, IL, USA
Tverberg’s theorem states that a set of n points in ℝ^d can be partitioned into ⌈n/(d+1)⌉ sets whose convex hulls all intersect. A point in the intersection (aka Tverberg point) is a centerpoint, or high-dimensional median, of the input point set. While randomized algorithms exist to find centerpoints with some failure probability, a partition for a Tverberg point provides a certificate of its correctness.
Unfortunately, known algorithms for computing exact Tverberg points take n^{O(d²)} time. We provide several new approximation algorithms for this problem, which improve running time or approximation quality over previous work. In particular, we provide the first strongly polynomial (in both n and d) approximation algorithm for finding a Tverberg point.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol204-esa2021/LIPIcs.ESA.2021.51/LIPIcs.ESA.2021.51.pdf
Geometric spanners
vertex failures
robustness