  We consider online algorithms for the $k$-server problem on trees. There is a
$k$-competitive algorithm for this problem, and it is the best competitive
ratio. M. Chrobak and L. Larmore provided it. At the same time, the existing
implementation has $O(n)$ time complexity for processing a query and $O(n)$ for
prepossessing, where $n$ is the number of nodes in a tree. Another
implementation of the algorithm has $O(k^2+k\log n)$ time complexity for
processing a query and $O(n\log n)$ for prepossessing. We provide a new
time-efficient implementation of the algorithm. It has $O(n)$ time complexity
for preprocessing and $O\left(k(\log n)^2\right)$ for processing a query.
