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We consider online algorithms for the k-server problem on trees of size n. Chrobak and Larmore proposed a k-competitive algorithm for this problem that has the optimal competitive ratio. However, the existing implementations have O (k² + k n) or O (k (n) ²) time complexity for processing a query, where n is the number of nodes. We propose a new time-efficient implementation of this algorithm that has O (n) time complexity for preprocessing and O (k k) time for processing a query. The new algorithm is faster than both existing algorithms and the time complexity for query processing does not depend on the tree size.
Khadiev et al. (Thu,) studied this question.