Improved Algorithms for Edge Colouring in the W-Streaming Model

Abstract

In the W-streaming model, an algorithm is given $O(n\mathrm{polylog}n)$ space and must process a large graph of up to $O(n^2)$ edges. In this short note we give two algorithms for edge colouring under the W-streaming model. For edge colouring in W-streaming, a colour for every edge must be determined by the time all the edges are streamed. Our first algorithm uses $\Delta +o(\Delta )$ colours in $O(n{\log }^{2}n)$ space when the edges arrive according to a uniformly random permutation. The second algorithm uses $(1+o(1)){\Delta }^2/s$ colours in $\tilde{O}(ns)$ space when edges arrival adversarially.

To appear in SOSA21. Updated to contain references to relevant work from SODA21