On the Advice Complexity of Online Unit Clustering

TL;DR

This paper investigates the advice complexity of online unit clustering in metric spaces, providing linear bounds on the amount of advice needed for optimal clustering in Euclidean and integer lattices.

Contribution

It establishes linear upper and lower bounds on advice complexity for 1-competitive online unit clustering algorithms in Euclidean and integer grid spaces.

Findings

Linear bounds on advice complexity in Euclidean space

Linear bounds on advice complexity in integer lattice space

Insights into the amount of advice needed for optimal online clustering

Abstract

In online unit clustering, points of a metric space arriving one by one must be partitioned into clusters of diameter at most 1, where the cost is the number of clusters. This paper gives linear upper and lower bounds on the advice complexity of 1-competitive online unit clustering algorithms, in terms of the number of points in $\mathbb{R}^d$ and $\mathbb{Z}^d$.