License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.14
URN: urn:nbn:de:0030-drops-115104
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11510/
Bienkowski, Marcin ;
Jez, Lukasz ;
Schmidt, Pawel
Slaying Hydrae: Improved Bounds for Generalized k-Server in Uniform Metrics
Abstract
The generalized k-server problem is an extension of the weighted k-server problem, which in turn extends the classic k-server problem. In the generalized k-server problem, each of k servers s_1, ..., s_k remains in its own metric space M_i. A request is a tuple (r_1,...,r_k), where r_i in M_i, and to service it, an algorithm needs to move at least one server s_i to the point r_i. The objective is to minimize the total distance traveled by all servers.
In this paper, we focus on the generalized k-server problem for the case where all M_i are uniform metrics. We show an O(k^2 * log k)-competitive randomized algorithm improving over a recent result by Bansal et al. [SODA 2018], who gave an O(k^3 * log k)-competitive algorithm. To this end, we define an abstract online problem, called Hydra game, and we show that a randomized solution of low cost to this game implies a randomized algorithm to the generalized k-server problem with low competitive ratio.
We also show that no randomized algorithm can achieve competitive ratio lower than Omega(k), thus improving the lower bound of Omega(k / log^2 k) by Bansal et al.
BibTeX - Entry
@InProceedings{bienkowski_et_al:LIPIcs:2019:11510,
author = {Marcin Bienkowski and Lukasz Jez and Pawel Schmidt},
title = {{Slaying Hydrae: Improved Bounds for Generalized k-Server in Uniform Metrics}},
booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)},
pages = {14:1--14:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-130-6},
ISSN = {1868-8969},
year = {2019},
volume = {149},
editor = {Pinyan Lu and Guochuan Zhang},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2019/11510},
URN = {urn:nbn:de:0030-drops-115104},
doi = {10.4230/LIPIcs.ISAAC.2019.14},
annote = {Keywords: k-server, generalized k-server, competitive analysis}
}
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Keywords: |
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k-server, generalized k-server, competitive analysis |
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Collection: |
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30th International Symposium on Algorithms and Computation (ISAAC 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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28.11.2019 |
