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

2026-03-12

AI Summary

This work proposes a deterministic distributed algorithm for minimum spanning tree (MST) construction that simultaneously achieves optimal time, communication, and memory efficiency—a balance not attained by existing approaches. The algorithm operates in $O(D + \sqrt{n})$ time with near-linear message complexity while reducing per-node memory usage to $O(\log n)$, the first such result to concurrently optimize all three metrics. This advance is enabled by a novel distributed control structure and a lightweight information aggregation mechanism that jointly minimize local state maintenance and inter-node communication overhead. Beyond resolving the longstanding trade-off in MST algorithms, the framework generalizes to broader distributed aggregation tasks, making it particularly suitable for large-scale, resource-constrained network environments.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Content-based information diffusion

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.

Problem

• minimum spanning tree
• distributed algorithms
• memory efficiency
• message complexity
• time complexity

Innovation

• minimum spanning tree
• distributed algorithm
• memory-efficient
• time-optimal
• partwise aggregation