LAUSR

In this paper, we show that there is a $$\frac{5}{2}\ell \cdot \ln (1+k)$$52ℓ·ln(1+k)-competitive randomized algorithm for the k-sever problem on weighted Hierarchically Separated Trees (HSTs) with depth $$\ell $$ℓ when $$n=k+1$$n=k+1 where n is the number of points in the metric space, which improved previous best competitive ratio $$12 \ell \ln (1+4\ell (1+k))$$12ℓln(1+4ℓ(1+k)) by Bansal et al. (FOCS, pp 267–276, 2011).