A synchronizer with low memory overhead

A new message-delaying version of synchronizer γ, named ζ, is presented. Synchronizer ζ ensures that original-protocol messages received by a node from nodes in the same cluster are never early, and thus, no buffers for their temporary storage are necessary. Only original-protocol messages on edges leading to nodes of other clusters (external edges) may be early. The z-partition algorithm is introduced to reduce the number of external edges connected to each node, thus reducing the memory overhead of ζ. For an arbitrary z, this algorithm ensures that the external degree of each node is no more than [|V|/z]-1. The z-partition algorithm increases the time complexity of ζ to O(z+log_k |V|) per pulse. The tradeoff between memory overhead and time complexity achieved by the z-partition algorithm is optimal