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COMGEO
2010
ACM

Approximate centerpoints with proofs

13 years 11 months ago
Approximate centerpoints with proofs
We present the IteratedTverberg algorithm, the first deterministic algorithm for computing an approximate centerpoint of a set S Rd with running time subexponential in d. The algorithm is a derandomization of the IteratedRadon algorithm of Clarkson et al and is guaranteed to terminate with an O(1/d2 )-center. Moreover, it returns a polynomial-time checkable proof of the approximation guarantee, despite the coNP-Completenes of testing centerpoints in general. We also explore the use of higher order Tverberg partitions to improve the runtime of the deterministic algorithm and improve the approximation guarantee for the randomized algorithm. In particular, we show how to improve the O(1/d2 )-center of the IteratedRadon algorithm to O(1/d r r-1 ) for a cost of O((rd)d
Gary L. Miller, Donald Sheehy
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where COMGEO
Authors Gary L. Miller, Donald Sheehy
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