A 2-Approximation Algorithm for Data-Distributed Metric k-Center

TL;DR

This paper presents a 2-approximation algorithm for the data-distributed metric k-center problem, achieving tight bounds in sublinear k scenarios and applicable to models like MPC.

Contribution

It introduces a novel 2-approximation algorithm for data-distributed metric k-center, extending the classical NP-hard problem to distributed settings with tight bounds.

Findings

Achieves a tight 2-approximation ratio for sublinear k.

Applicable to multiple distributed models including MPC.

Extends classical k-center solutions to data-distributed environments.

Abstract

In a metric space, a set of point sets of roughly the same size and an integer $k\geq 1$ are given as the input and the goal of data-distributed $k$-center is to find a subset of size $k$ of the input points as the set of centers to minimize the maximum distance from the input points to their closest centers. Metric $k$-center is known to be NP-hard which carries to the data-distributed setting. We give a $2$-approximation algorithm of $k$-center for sublinear $k$ in the data-distributed setting, which is tight. This algorithm works in several models, including the massively parallel computation model (MPC).