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arXiv · 1712.05007

Greedy spanners are optimal in doubling metrics

Glencora Borradaile·Hung Le·Christian Wulff-Nilsen
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Abstract

We show that the greedy spanner algorithm constructs a $(1+\epsilon)$-spanner of weight $\epsilon^{-O(d)}w(\mathrm{MST})$ for a point set in metrics of doubling dimension $d$, resolving an open problem posed by Gottlieb. Our result generalizes the result by Narasimhan and Smid who showed that a point set in $d$-dimension Euclidean space has a $(1+\epsilon)$-spanner of weight at most $\epsilon^{-O(d)}w(\mathrm{MST})$. Our proof only uses the packing property of doubling metrics and thus implies a much simpler proof for the same result in Euclidean space.

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Glencora Borradaile, Hung Le, Christian Wulff-Nilsen. 2017-12-13. Greedy spanners are optimal in doubling metrics. https://arxiv.org/abs/1712.05007

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