The reverse greedy algorithm for the metric k-median problem

TL;DR

This paper analyzes the Reverse Greedy algorithm for the metric k-median problem, establishing bounds on its approximation ratio and demonstrating its effectiveness in selecting facilities to minimize total customer distance.

Contribution

It provides theoretical bounds on the approximation ratio of the RGreedy algorithm for the metric k-median problem, a previously less-understood approach.

Findings

Approximation ratio is between Ω(log n / log log n) and O(log n) for metric distances.

The analysis offers new insights into the performance of reverse greedy methods.

The results improve understanding of facility location algorithms in metric spaces.

Abstract

The Reverse Greedy algorithm (RGreedy) for the k-median problem works as follows. It starts by placing facilities on all nodes. At each step, it removes a facility to minimize the resulting total distance from the customers to the remaining facilities. It stops when k facilities remain. We prove that, if the distance function is metric, then the approximation ratio of RGreedy is between ?(log n/ log log n) and O(log n).