A Fast Algorithm for Online k-servers Problem on Trees

05/31/2020

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by   Kamil Khadiev, et al.

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We consider online algorithms for the k-servers problem on trees. There is an k-competitive algorithm for this problem, and it is the best competitive ratio. M. Chrobak and L. Larmore suggested it. At the same time, the existing implementation has O(n) time complexity, where n is a number of nodes in a tree. We suggest a new time-efficient implementation of the algorithm. It has O(n) time complexity for preprocessing and O(k(log n)^2) for processing a query.