Time, Message and Memory-Optimal Distributed Minimum Spanning Tree and Partwise Aggregation

Memory-(in)efficiency is a crucial consideration that oftentimes prevents deployment of state-of-the-art distributed algorithms in real-life modern networks. In the context of the MST problem, roughly speaking, there are three types of algorithms. The algorithm of Gallager-Humblet-Spira and its versions are memory- and message- efficient, but their running time is at least linear in the number of vertices $n$, even when the unweighted diameter $D$ is much smaller than $n$. The algorithm of Garay-Kutten-Peleg and its versions are time-efficient, but not message- or memory-efficient. The more recent algorithms of are time- and message-efficient, but are not memory-efficient. As a result, GHS-type algorithms are much more prominent in real-life applications than time-efficient ones. In this paper we develop a deterministic time-, message- and memory-efficient algorithm for the MST problem. It is also applicable to the more general partwise aggregation problem. We believe that our techniques will be useful for devising memory-efficient versions for many other distributed problems.