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

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