We give a simple, local process for nodes in an undirected graph to form non-adjacent clusters that (1) have at most a polylogarithmic diameter and (2) contain at least half of all vertices. Efficient deterministic distributed clustering algorithms for computing strong-diameter network decompositions and other key tools follow immediately. Overall, our process is a direct and drastically simplified way for computing these fundamental objects.
@article{arxiv.2210.11784,
title = {A Simple Deterministic Distributed Low-Diameter Clustering},
author = {Václav Rozhoň and Bernhard Haeupler and Christoph Grunau},
journal= {arXiv preprint arXiv:2210.11784},
year = {2022}
}