Unicast, multicast, and broadcast in enhanced Fibonacci cubes

The enhanced Fibonacci cube (EFC) is defined based on the sequence F_n=2F_n-2+2F_n-4. It contains the Fibonacci cube as a subgraph and maintains virtually all the desirable properties of the Fibonacci cube, and it also possesses properties such as the Hamiltonian property that the Fibonacci cube does not have. In this paper, we study data routing, namely, unicast, multicast and broadcast in the enhanced Fibonacci cube. The time and traffic steps are used to measure the efficiency of the routing algorithms. The unicast algorithm, which uses a Hamming distance path for any two nodes in EFC, is time and traffic optimal. The broadcast algorithm which employs the enhanced Fibonacci tree is traffic optimal and near time optimal. Two heuristic multicast algorithms are proposed which are based on an enhanced Fibonacci tree and a Hamiltonian cycle, respectively