Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Khadiev, Kamil, Yagafarov, Maxim
Institution: Kazan Federal University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Kazan Federal University
Award: G1709152956
OpenAlex ID: W3032877845