Optimization of logical rings for multi-hop transmissions in WDM optical star networks

In this paper, we present a multi-hop scheduling algorithm for the All-to-All Broadcast (AAB) problem in Wavelength Division Multiplexed (WDM) optical star networks with N nodes. To decrease the packet delay in packet transmissions, our scheduling algorithm will limit the hop distance to a constant ρ. We transfer the ρ-hop AAB problem to the Hamiltonian cycles problem and then generate the logical rings for physical packet transmissions. In order to minimize the scheduling length, the problem of selection of logical rings is to minimize the number of tuning operations to reduce the influence of tuning latency δ for the AAB problem. We propose a 2-approximation algorithm that needs only 2⌈(N − 1)/ ρ  ⌉ tuning operations in an AAB scheduling. When ρ<δ+δ2-8δ2, the schedule length of our algorithm will be shorter than that of the optimal single-hop scheduling algorithm.