Abstract
We consider the backup placement problem, defined as follows. Some nodes (processors) in a given network have objects (e.g., files, tasks) whose backups should be stored in additional nodes for increased fault resilience. To minimize the disturbance in case of a failure, it is required that a backup copy should be located at a neighbor of the primary node. The goal is to find an assignment of backup copies to nodes which minimizes the maximum load (number or total size of backup copies) over all nodes in the network. It is known that a natural selfish local improvement policy has approximation ratio Ω(log n/ log log n) ; we show that it may take this policy Ω(n) time to reach equilibrium in the distributed setting. Our main result in this paper is a randomized distributed algorithm which finds a placement in polylogarithmic time and achieves approximation ratio O(lognloglogn). We obtain this result using a randomized distributed approximation algorithm for f-matching in bipartite graphs that may be of independent interest.
| Original language | English |
|---|---|
| Pages (from-to) | 83-98 |
| Number of pages | 16 |
| Journal | Distributed Computing |
| Volume | 31 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Apr 2018 |
Bibliographical note
Funding Information:A preliminary version was presented at the 27th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) 2015. Magnús M. Halldórsson supported in part by Icelandic Research Fund (Grants Nos. 120032011 and 152679-051). Sven Köhler supported in part by the Sustainability Center Freiburg, Germany, which is a cooperation of the Fraunhofer Society and the University of Freiburg and is supported by Grants from the Baden-Württemberg Ministry of Economics and the Baden-Württemberg Ministry of Science, Research and the Arts. Boaz Patt-Shamir supported in part by the Ministry of Science, Technology and Space, Israel (Grant No. 3-10996) and the Israel Science Foundation (Grants No. 1444/14). Dror Rawitz supported in part by the Ministry of Science, Technology and Space, Israel (Grant No. 3-10996) and the Israel Science Foundation (Grant No. 497/14).
Funding Information:
A preliminary version was presented at the 27th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) 2015. Magn?s M. Halld?rsson supported in part by Icelandic Research Fund (Grants Nos.?120032011 and 152679-051). Sven K?hler supported in part by the Sustainability Center Freiburg, Germany, which is a cooperation of the Fraunhofer Society and the University of Freiburg and is supported by Grants from the Baden-W?rttemberg Ministry of Economics and the Baden-W?rttemberg Ministry of Science, Research and the Arts. Boaz Patt-Shamir supported in part by the Ministry of Science, Technology and Space, Israel (Grant No.?3-10996) and the Israel Science Foundation (Grants No.?1444/14). Dror Rawitz supported in part by the Ministry of Science, Technology and Space, Israel (Grant No.?3-10996) and the Israel Science Foundation (Grant No.?497/14).
Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.