Greedy Is Good: An Empirical Evaluation of Three Algorithms for Online Bottleneck Matching

Barbara M. Anthony1, Christine Harbour1, Jordan King1
1Mathematics and Computer Science Department, Southwestern University, Georgetown, Texas, USA

Abstract

We empirically evaluate the performance of three approximation algorithms for the online bottleneck matching problem. In this matching problem, \( k \) server-vertices lie in a metric space and \( k \) request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. The goal is to minimize the maximum distance between any request and its assigned server. We consider the naïve \textsc{Greedy} algorithm, as well as \textsc{Permutation} and \textsc{Balance}, each of which were constructed to counter certain challenges in the online problem. We analyze the performance of each algorithm on a variety of data sets, considering each both in the original model, where applicable, and in the resource augmentation setting when an extra server is introduced at each server-vertex. While no algorithm strictly dominates, \textsc{Greedy} frequently performs the best, and thus is recommended due to its simplicity.