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

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 $\Omega (1)$.

References in corpus (1)

• A lower bound for metric 1-median selection