Faster than Optimal Snapshots (for a While)

This paper presents a breakthrough in shared memory computation by giving an implementation of a snapshot object for n processes that has O(log b log n) step complexity for update operations and O(log b) step complexity for scan operations, where b is the number of updates. The algorithm uses only reads and writes. For polynomially many updates, this is an exponential improvement on the previous linear snapshot algorithms, and it overcomes the existing Ω(n) lower bound by having the step complexity depend on the number of updates. The key to this implementation is the construction of a new object consisting of a pair of max registers that supports a scan operation. Applications of this construction include an implementation of a limited-use generalized counter with polylogarithmic step complexity. This can be used, for example, to monitor the number of active processes, which is crucial to adaptive algorithms. ∗Yale University, Department of Computer Science. Supported in part by NSF grant CCF-0916389. †Technion. Supported in part by ISF grant 1227/10. ‡Massachusetts Institute of Technology, Computer Science and Artificial Intelligence Laboratory. Supported by the Simons Postdoctoral Fellows Program. §University of Toronto, Department of Computer Science. Supported in part by the Natural Science and Engineering Research Council of Canada.