The time complexity of updating snapshot memories

Abstract

An atomic snapshot memory enables a set of processes, called scanners, to obtain a consistent picture of the shared memory while other processes, called updaters, keep updating memory locations concurrently. Implementations of atomic snapshot memory are key tools in designing distributed protocols in shared memory systems. Such an implementation consists of two protocols: an update protocol and a scan protocol, executed by updaters and scanners, respectively. Clearly, the time complexity of the scan protocol is at least linear, and there exists an implementation which matches the lower bound. In this paper we show that the time complexity of an optimal update protocol is Θ( n), where n is the number of updaters and scanners. The time complexity of the scan protocol remains O( n log n). The lower bound is valid even when the updates are serial, meaning, no two updates overlap. In addition, the lower bound does not assume that the protocols are uniform or that the processors use bounded registers.