  For any $\epsilon>0$, Laue and Matijevi\'{c} [CCCG'07, IPL'08] give a PTAS
for finding a $(1+\epsilon)$-approximate solution to the $k$-hop MST problem in
the Euclidean plane that runs in time $(n/\epsilon)^{O(k/\epsilon)}$. In this
paper, we present an algorithm that runs in time $(n/\epsilon)^{O(\log k
\cdot(1/\epsilon)^2\cdot\log^2(1/\epsilon))}$. This gives an improvement on the
dependency on $k$ on the exponent, while having a worse dependency on
$\epsilon$. As in Laue and Matijevi\'{c}, we follow the framework introduced by
Arora for Euclidean TSP. Our key ingredients include exponential distance
scaling and compression of dynamic programming state tables.
