Analysis of Randomized Protocols for Conflict-Free Distributed Access
We study the following distributed access problem which arises naturally in many settings: given a set of n data items shared among n nodes in a distributed network, all nodes want to access all (or a subset of) the items residing on different nodes in a conflict-free manner. In addition, items may move from one node to the other during access. Our goal is to design distributed protocols so that all nodes access all the desired items as quickly as possible, while at the same time not overloading the storage space of any one node. Using centralized coordination among the nodes it is easy to design an optimal scheme in which all nodes can access all the items in n−1 steps storing only one item at any time. We show that a simple randomized distributed protocol performs almost as well as the optimal (centralized) scheme but with no coordination overhead. Our protocol takes O(n) time with high probability to access all n items which is asymptotically as good as the optimal centralized scheme. The protocol guarantees that the maximum load (the maximum number of items stored in any node) at any time is at most O(log n/log log n) with high probability which is only slightly larger compared to the Ω(1) load of the optimal scheme. Our analysis involves a stochastic analysis of a “balls into bins” problem in a dynamic setting where balls (data items) move into bins (nodes) on request and we study the time and load requirements to move all the balls to the requested bins.
KeywordsRandomized distributed protocols Conflict-free access
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