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arXiv · 1702.03106

A Las Vegas approximation algorithm for metric $1$-median selection

Ching-Lueh Chang
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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 $O(n/\epsilon^2)$ time for each constant $\epsilon>0$. Inheriting Indyk's algorithm, our algorithm outputs a $(1+\epsilon)$-approximate $1$-median in $O(n/\epsilon^2)$ time with probability $\Omega(1)$.

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Ching-Lueh Chang. 2017-02-10. A Las Vegas approximation algorithm for metric $1$-median selection. https://arxiv.org/abs/1702.03106

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