On Underlay-Aware Self-Stabilizing Overlay Networks

TL;DR

This paper introduces a self-stabilizing protocol for overlay networks that constructs the MST considering an underlying weighted tree, ensuring correctness and stabilization within quadratic asynchronous rounds.

Contribution

It presents a novel self-stabilizing protocol for MST construction in underlay-aware overlay networks modeled by weighted trees.

Findings

Protocol stabilizes after O(N^2) asynchronous rounds.

Works correctly under asynchronous and non-FIFO message delivery.

Constructs MST based on shortest path weights in the underlying tree.

Abstract

We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of their shortest path in the tree. We rigorously prove that our protocol works correctly under asynchronous and non-FIFO message delivery. Further, the protocol stabilizes after $\mathcal{O}(N^2)$ asynchronous rounds where $N$ is the number of nodes in the overlay.