Atomic Snapshots in O(log3 n) Steps Using Randomized Helping

A randomized construction of single-writer snapshot objects from atomic registers is given. The cost of each snapshot operation is O(log3 n) atomic register steps with high probability, where n is the number of processes, even against an adaptive adversary. This is an exponential improvement on the linear cost of the previous best known snapshot construction [9, 10] and on the linear lower bound for deterministic constructions [11], and does not require limiting the number of updates as in previous sublinear constructions [4]. One of the main ingredients in the construction is a novel randomized helping technique that allows out-of-date processes to obtain up-to-date information. Our construction can be adapted to implement snapshots in a message-passing system. While a direct adaptation using the Attiya-Bar-Noy-Dolev construction gives a cost of O(log3 n) time and O(n log3 n) messages per operation with high probability, we show that exploiting the inherent parallelism of a message-passing system can eliminate the need for randomized helping and reduce the complexity to O(log2 n) time and O(n log2 n) messages per operation in the worst case. This implementation includes an O(1)-time, O(n)-message construction of an unbounded-value max register that may be of independent interest. ∗A preliminary version of this work appeared in the proceedings of the 27th International Symposium on Distributed Computing (DISC), pages 254–268, 2013. We mention that the implementation of the unbounded max array given in the conference version does not give the claimed step complexity, and is replaced here by a different construction. †Yale University, Department of Computer Science. Supported in part by NSF grants CCF-0916389, CCF-1637385, and CCF-1650596. ‡Technion, Department of Computer Science.