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arXiv · 1406.4433

Uniform multicommodity flow in the hypercube with random edge capacities

Colin McDiarmid·Alex Scott·Paul Withers
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Abstract

We give two results for multicommodity flows in the $d$-dimensional hypercube ${Q}^d$ with independent random edge capacities distributed like $C$ where $\Pr[C>0]>1/2$. Firstly, with high probability as $d \rightarrow \infty$, the network can support simultaneous multicommodity flows of volume close to $E[C]$ between all antipodal vertex pairs. Secondly, with high probability, the network can support simultaneous multicommodity flows of volume close to $2^{1-d} E[C]$ between all vertex pairs. Both results are best possible.

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Colin McDiarmid, Alex Scott, Paul Withers. 2014-06-17. Uniform multicommodity flow in the hypercube with random edge capacities. https://arxiv.org/abs/1406.4433

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