Proceedings
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

Competitive Algorithms for Generalized k-Server in Uniform Metrics

Abstract

The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server si lies in its own metric space Mi. A request is a k-tuple r = (r1, r2, …, rk) and to serve it, we need to move some server si to the point riMi, and the goal is to minimize the total distance traveled by the servers. Despite much work, no f(k)-competitive algorithm is known for the problem for k > 2 servers, even for special cases such as uniform metrics and lines.
Here, we consider the problem in uniform metrics and give the first f(k)-competitive algorithms for general k. In particular, we obtain deterministic and randomized algorithms with competitive ratio k · 2k and O(k3 log k) respectively. Our deterministic bound is based on a novel application of the polynomial method to online algorithms, and essentially matches the long-known lower bound of 2k – 1. We also give a 22O(k)-competitive deterministic algorithm for weighted uniform metrics, which also essentially matches the recent doubly exponential lower bound for the problem.

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cover image Proceedings
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
Pages: 992 - 1001
Editor: Artur Czumaj, University of Warwick, United Kingdom
ISBN (Online): 978-1-61197-503-1

History

Published online: 2 January 2018

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*
This work was supported by NWO grant 639.022.211, ERC consolidator grant 617951, and NWO Veni project 639.021.438

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