A Simple Deterministic Distributed Low-Diameter Clustering

TL;DR

This paper introduces a straightforward deterministic distributed method for clustering nodes in a graph into low-diameter, non-adjacent groups, enabling efficient computation of network decompositions and related tools.

Contribution

It presents a simple, local, deterministic process for creating low-diameter clusters that cover at least half the vertices, simplifying prior complex algorithms.

Findings

Clusters have polylogarithmic diameter

At least half of all vertices are included in the clusters

Enables efficient deterministic algorithms for network decompositions

Abstract

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.