Compact routing on euclidian metrics

We consider the problem of designing a compact communication network that supports efficient routing in an Euclidean plane. Our network design and routing scheme achieves 1+ε stretch, logarithmic diameter, and constant out degree. This improves upon the best known result so far that requires a logarithmic out-degree. Furthermore, our scheme is asymptotically optimal in Euclidean metrics whose diameter is polynomial.

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