For sparse traffic with k pairs in an N x N torus, the minimal worst-case load achievable by any oblivious routing is approximately sqrt(2k)/4, with a new scheme attaining this bound and outperforming Valiant load balancing.
In problem (21), we interpretλ(d, t, i, e) as the cost of using edge(i, i+e)in a route totunder traffic matrixd
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Optimal Oblivious Load-Balancing for Sparse Traffic in Large-Scale Satellite Networks
For sparse traffic with k pairs in an N x N torus, the minimal worst-case load achievable by any oblivious routing is approximately sqrt(2k)/4, with a new scheme attaining this bound and outperforming Valiant load balancing.