# 2-Edge-Connectivity and 2-Vertex-Connectivity of an Asynchronous Distributed Network

## TL;DR

This paper introduces a self-stabilizing algorithm for determining 2-edge and 2-vertex connectivity in asynchronous distributed networks, leveraging a depth-first search approach to ensure fault tolerance and network robustness.

## Contribution

It presents a novel, non-composite self-stabilizing algorithm for 2-edge and 2-vertex connectivity, with optimal time and space complexities based on depth-first search.

## Key findings

- Algorithm stabilizes in O(dnΔ) rounds
- Uses O(n log Δ) bits per processor
- Effective for asynchronous distributed networks

## Abstract

Self-stabilization for non-masking fault-tolerant distributed system has received considerable research interest over the last decade. In this paper, we propose a self-stabilizing algorithm for 2-edge-connectivity and 2-vertex-connectivity of an asynchronous distributed computer network. It is based on a self-stabilizing depth-first search, and is not a composite algorithm in the sense that it is not composed of a number of self-stabilizing algorithms that run concurrently. The time and space complexities of the algorithm are the same as those of the underlying self-stabilizing depth-first search algorithm which are O(dn\Delta) rounds and O(n\log \Delta) bits per processor, respectively, where \Delta (<= n) is an upper bound on the degree of a node, d (<= n) is the diameter of the graph, and n is the number of nodes in the network.