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arXiv · 2010.14560

Improved Algorithms for Edge Colouring in the W-Streaming Model

Moses Charikar·Paul Liu
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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 $Δ+ o(Δ)$ colours in $O(n \log^2 n)$ space when the edges arrive according to a uniformly random permutation. The second algorithm uses $(1 + o(1))Δ^2 / s$ colours in $\tilde{O}(n s)$ space when edges arrival adversarially.

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Moses Charikar, Paul Liu. 2020-10-29. Improved Algorithms for Edge Colouring in the W-Streaming Model. https://arxiv.org/abs/2010.14560

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