Distributed backup placement in networks

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.