A deterministic sublinear-time nonadaptive algorithm for metric $1$-median selection

TL;DR

This paper presents a deterministic, nonadaptive algorithm for selecting a 1-median in metric spaces that achieves a trade-off between approximation ratio and runtime, generalizing previous work.

Contribution

It introduces a new deterministic, nonadaptive algorithm with a tunable approximation ratio and runtime, extending Chang's approach to broader settings.

Findings

Runs in $O(hn^{1+1/h})$ time for any positive integer $h$

Achieves a $(2h)$-approximation ratio

Generalizes previous algorithms by Chang

Abstract

We give a deterministic $O(hn^{1+1/h})$-time $(2h)$-approximation nonadaptive algorithm for $1$-median selection in $n$-point metric spaces, where $h\in\mathbb{Z}^+\setminus\{1\}$ is arbitrary. Our proof generalizes that of Chang.