A Ptas for K-Hop Mst on the Euclidean Plane: Improving Dependency on K

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