On Distributed Colouring of Hyperbolic Random Graphs

TL;DR

This paper investigates the efficiency of distributed graph coloring algorithms on hyperbolic random graphs, a model that reflects real-world network properties, focusing on rounds needed and color space size.

Contribution

It provides the first analysis of distributed coloring performance specifically tailored to hyperbolic random graphs, bridging theory and realistic network models.

Findings

Analyzes rounds needed for coloring HRGs in distributed algorithms

Determines size of color space required for effective coloring

Highlights differences from worst-case graph coloring scenarios

Abstract

We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree distributions and large clustering coefficients. Motivated by the shift from worst-case analysis to more realistic network models, we study the number of rounds and size of the colour space required to colour HRGs in the distributed setting.