A New Self-Stabilizing Minimum Spanning Tree Construction with Loop-free Property

TL;DR

This paper introduces a new self-stabilizing algorithm for constructing and maintaining a minimum spanning tree in distributed networks, ensuring loop-free operation during dynamic changes with improved efficiency.

Contribution

It presents a self-stabilizing MST protocol that requires fewer assumptions, guarantees loop-free updates during dynamic changes, and achieves optimal time and space complexity.

Findings

Fewer system hypotheses needed, no knowledge of network size required.

Guarantees loop-free spanning tree during dynamic edge cost changes.

Achieves best known time and space complexity for self-stabilizing MST protocols.

Abstract

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known ap- proaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date.