This paper shows that the memory overhead of distributed snapshots is unbounded. Several techniques are suggested for bounding it: bounded memory-overhead versions of distributed snapshots for specific problems, like termination detection and deadlock detection; use of alternative protocols; or use of synchronizers or schedulers in order to limit the photographed protocol to executions whose distributed snapshot requires bounded memory. Each solution is discussed in detail, and its memory overhead is analyzed. © 1999 John Wiley & Sons, Inc. Networks 34: 11–17, 1999

A new message-delaying version of synchronizer /spl gamma/, named /spl zeta/, is presented. Synchronizer /spl zeta/ 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 /spl zeta/. 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 /spl zeta/ to O(z+log/sub k/ |V|) per pulse. The tradeoff between memory overhead and time complexity achieved by the z-partition algorithm is optimal.>

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