Improved Bounds on Nonblocking 3-Stage Clos Networks

@article{Correa2007ImprovedBO,
  title={Improved Bounds on Nonblocking 3-Stage Clos Networks},
  author={J. Correa and M. Goemans},
  journal={SIAM J. Comput.},
  year={2007},
  volume={37},
  pages={870-894}
}
We consider a generalization of edge coloring bipartite graphs in which every edge has a weight in $[0,1]$ and the coloring of the edges must satisfy that the sum of the weights of the edges incident to a vertex $v$ of any color must be at most 1. For unit weights, Konig's theorem says that the number of colors needed is exactly the maximum degree. For this generalization, we show that $2.557 n + o(n)$ colors are sufficient, where $n$ is the maximum total weight adjacent to any vertex… Expand
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