Complexity Analysis of Data Routing Algorithms in Extended Lucas Cube Networks

Abstract

We introduce a class of novel interconnection topologies called extended Lucas cube (ELC). The ELC is an induced subgraph of hypercube defined in terms of Fibonacci strings. This model is classified as a member of the Fibonacci cube family. ELC can serve as a framework for studying degraded hypercube due to faulty nodes or links. ELC maintains virtually almost all the desirable properties of hypercube. The focus of this paper is on the data communication aspects in the ELC. In this paper, we study data routing algorithms in the ELC, namely, unicast, broadcast and multicast algorithms. An important property of any message routing algorithm is to avoid deadlock. The unicast algorithm always succeeds in finding a path between them and ensures deadlock free in ELC. The time and traffic steps are used to measure the efficiency of routing algorithms. The unicast algorithm for ELC, which uses a Hamming distance path for any two nodes, is time and traffic optimal. The broadcast algorithm which employs the extended Lucas tree is traffic optimal and near time optimal. Two multicast algorithms are presented; they are based on an extended Lucas tree and a Hamiltonian cycle, respectively.