# Node-Independent Spanning Trees in Gaussian Networks

## TL;DR

This paper introduces constructions of node-independent spanning trees in Gaussian networks, enabling fault-tolerant and secure message routing with improved performance due to their smaller diameter.

## Contribution

The paper presents novel methods for constructing node-independent spanning trees specifically in dense Gaussian networks, along with routing and fault-tolerant algorithms.

## Key findings

- Constructed node-independent spanning trees in Gaussian networks.
- Designed routing algorithms for fault-tolerance and security.
- Developed parallel algorithms for tree construction.

## Abstract

Message broadcasting in networks could be carried over spanning trees. A set of spanning trees in the same network is node independent if two conditions are satisfied. First, all trees are rooted at node $r$. Second, for every node $u$ in the network, all trees' paths from $r$ to $u$ are node-disjoint, excluding the end nodes $r$ and $u$. Independent spanning trees have applications in fault-tolerant communications and secure message distributions. Gaussian networks and two-dimensional toroidal networks share similar topological characteristics. They are regular of degree four, symmetric, and node-transitive. Gaussian networks, however, have relatively lesser network diameter that could result in a better performance. This promotes Gaussian networks to be a potential alternative for two-dimensional toroidal networks. In this paper, we present constructions for node independent spanning trees in dense Gaussian networks. Based on these constructions, we design routing algorithms that can be used in fault-tolerant routing and secure message distribution. We also design fault-tolerant algorithms to construct these trees in parallel.