Optimal propagation-based protocols implementing causal memories

Ensuring causal consistency in a Distributed Shared Memory (DSM) means all operations executed at each process will be compliant to a causality order relation. This paper first introduces an optimality criterion for a protocol P, based on a complete replication of variables at each process and propagation of write updates, that enforces causal consistency. This criterion measures the capability of a protocol to update the local copy as soon as possible while respecting causal consistency. Then we present an optimal protocol built on top of a reliable broadcast communication primitive and we show how previous protocols based on complete replication presented in the literature are not optimal. Interestingly, we prove that the optimal protocol embeds a system of vector clocks which captures the read/write semantics of a causal memory. From an operational point of view, an optimal protocol strongly reduces its message buffer overhead. Simulation studies show that the optimal protocol roughly buffers a number of messages of one order of magnitude lower than non-optimal ones based on the same communication primitive.