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

TL;DR

This paper introduces a deterministic distributed algorithm for the Minimum Spanning Tree problem that is simultaneously time-, message-, and memory-efficient, addressing a key limitation of existing algorithms and applicable to broader aggregation tasks.

Contribution

The paper presents the first deterministic algorithm that is efficient in time, message, and memory for distributed MST and partwise aggregation problems.

Findings

Achieves simultaneous efficiency in time, message, and memory.

Applicable to general partwise aggregation problems.

Potential to inspire memory-efficient solutions for other distributed algorithms.

Abstract

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.