Finding shortest paths in distributed loop networks

Abstract

Loop networks with hop connections offer smaller diameter, path lengths, alternative routes in paths and have better fault-tolerance. Such loop networks, known as distributed loops have potential applications in local area networks, parallel processing and multicomputer interconnection environment. The shortest path between any two nodes in a distributed loop network has been studied for specific hop sizes. Results exist for computing this in O(δ) time, where δ is the diameter of the distributed loop. But there exists no closed form for the diameter. In this paper we consider distributed loops of n nodes having hop connections and without any knowledge of diameter, obtain the shortest path in O( h g + log(h)) time, where h is the hop size and g is GCD( n, h).