Panconnectivity Algorithm for Eisenstein-Jacobi Networks

TL;DR

This paper introduces an algorithm to generate and verify panconnectivity in Eisenstein-Jacobi networks, ensuring the existence of cycles of various lengths between node pairs, which enhances understanding of network robustness.

Contribution

The paper presents a novel algorithm for establishing and proving panconnectivity in Eisenstein-Jacobi networks, with a detailed proof of correctness and a time complexity of O(n^4).

Findings

Algorithm successfully constructs all cycles of specified lengths.

Proves the network's panconnectivity property.

Provides complexity analysis of the algorithm.

Abstract

The cycles in an interconnection network are one of the communication types that are considered as a factor to measure the efficiency and reliability of the networks' topology. The network is said to be panconnected if there are cycles of length $l$ between two nodes u and v, for all l = d(u, v), d(u, v) +1, d(u, v) +2, ..., n-1 where d(u, v) is the shortest distance between u and v in a given network, and n is the total number of nodes in the network. In this paper, we propose an algorithm that generates and proves the panconnectivity of Eisenstein-Jacobi networks by constructing all cycles between any two nodes in the network of length l such that 3 <= l < n. The correctness of the proposed algorithm is given with the time complexity O(n^4).