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 data items shared among 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. The 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. We show that a simple randomized distributed protocol (Protocol 1 of the paper) performs almost as well as an 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 the same compared to the optimal scheme. The protocol guarantees that the maximum load of any processor 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