Overlay Topology as Random-Walk Cache

A probabilistic quorum system (PQS) allows distributed services to be replicated on only a subset (quorum) of servers. The replicas can be kept consistent with high levels of assurance as long as any two quorums intersect with very high probability. PQS thus provides a means to trade off levels of consistency against the scalability and efficiency of a quorum system. When quorums are constructed by choosing members of the subset uniformly at random, the non-intersection probability can be easily computed. On a distributed system with n servers, uniform sampling is often conducted using random walk of length O(log n). To collect multiple uniform samples naively would require as many random walks. A number of works have relied on analytical results based on the Chernoff bound to reduce the number of random walks needed to collect multiple samples. Controlled flooding is another efficient method to collect multiple samples. In this paper we evaluate both methods analytically and found that quorums formed using either method cannot satisfy the non-intersection probability bound associated with quorum formed by uniform sampling. Our contributions are: (1) to show that overlay topology can be constructed to cache multiple random walks, (2) to show that repeated use of this cache to obtain multiple uniform samples leads to degradation of sample uniformity over time, and (3) to propose and evaluate graph re-wiring as a simple method to keep the cache fresh, to take advantage of overhead reduction of random walk caching while alleviating the degradation in sample uniformity.