Metric $1$-median selection: Query complexity vs. approximation ratio

Ching-Lueh Chang

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arXiv · 1509.05662

Metric $1$-median selection: Query complexity vs. approximation ratio

Ching-Lueh Chang

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Abstract

Consider the problem of finding a point in a metric space $(\{1,2,\ldots,n\},d)$ with the minimum average distance to other points. We show that this problem has no deterministic $o(n^{1+1/(h-1)})$-query $(2h-Ω(1))$-approximation algorithms for any constant $h\in\mathbb{Z}^+\setminus\{1\}$.

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Ching-Lueh Chang. 2015-09-18. Metric $1$-median selection: Query complexity vs. approximation ratio. https://arxiv.org/abs/1509.05662

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