Independent Spanning Trees in Eisenstein-Jacobi Networks

TL;DR

This paper introduces new constructions of node- and edge-independent spanning trees in Eisenstein-Jacobi networks, enabling secure and fault-tolerant message routing in various applications.

Contribution

It presents two novel spanning tree constructions for Eisenstein-Jacobi networks, including edge-disjoint and non-edge-disjoint node-independent trees, with routing algorithms for fault tolerance.

Findings

Constructed three edge-disjoint node-independent spanning trees.

Constructed six node-independent spanning trees (not edge-disjoint).

Developed routing algorithms for secure, fault-tolerant communication.

Abstract

Spanning trees are widely used in networks for broadcasting, fault-tolerance, and securely delivering messages. Hexagonal interconnection networks have a number of real life applications. Examples are cellular networks, computer graphics, and image processing. Eisenstein-Jacobi (EJ) networks are a generalization of hexagonal mesh topology. They have a wide range of potential applications, and thus they have received researchers' attention in different areas among which interconnection networks and coding theory. In this paper, we present two spanning trees' constructions for Eisenstein-Jacobi (EJ). The first constructs three edge-disjoint node-independent spanning trees, while the second constructs six node-independent spanning trees but not edge disjoint. Based on the constructed trees, we develop routing algorithms that can securely deliver a message and tolerate a number of faults in point-to-point or in broadcast communications. The proposed work is also applied on higher dimensional EJ networks.