Emergent Mind
A Las Vegas approximation algorithm for metric $1$-median selection
(1702.03106)
Published Feb 10, 2017
in
cs.DS
Abstract
Given an $n$-point metric space, consider the problem of finding a point with the minimum sum of distances to all points. We show that this problem has a randomized algorithm that {\em always} outputs a $(2+\epsilon)$-approximate solution in an expected $O(n/\epsilon2)$ time for each constant $\epsilon>0$. Inheriting Indyk's algorithm, our algorithm outputs a $(1+\epsilon)$-approximate $1$-median in $O(n/\epsilon2)$ time with probability $\Omega(1)$.
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