Panconnectivity Algorithm for Eisenstein-Jacobi Networks
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Eisenstein-Jacobi (EJ) networks were proposed as an efficient interconnection network topology for parallel and distributed systems. They are based on Eisenstein-Jacobi integers modulo a = a+bρ, where 0 ≤ a ≤ b, and they are 6-regular symmetric networks and considered as a generalization of hexagonal networks. Most of the interconnection networks are modeled as graphs where the applications and functions of graph theory could be applied to. The cycles in a graph are one type of communications in interconnection networks 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 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 nodes u and v in a given network. In this paper, we investigate the panconnectivity problem in Eisenstein-Jacobi networks. The proposed algorithm constructs and proves the panconnectivity of a given Eisenstein-Jacobi network and its complexity is O(n^4). Simulation results are given to support the correctness of this work.
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