  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.
