Hypercube interconnection in TWDM optical passive star networks

This paper is concerned with optimal transmission schedules in a hypercube interconnection topology using the TWDM (time and wavelength division multiplexed) optical passive star network. Our model of the network consists of a set V of N nodes with N tunable transmitters and N fixed-tuned receivers (where each node is assigned a transmitter-receiver pair), k (=2^b for an integer b) wavelengths (each wavelength is shared by N/k receivers where N/k is an integer), and tuning time δ>0 (in units of time slot, for transmitters to tune from one wavelength to another). We assume that N is equal to the number of nodes in the hypercube, and that at any given time slot at most one transmission can be done per wavelength. An optimal transmission schedule in a hypercube interconnection is defined to be the one that schedules transmissions such that for each node v of the hypercube, v transmits once to each of its neighboring nodes within a repeating cycle of minimum length. We first construct an embedding of the n-dimensional hypercube Q_n in V such that for any node of Q_n, its n neighboring nodes are evenly partitioned into b groups where each group shares a wavelength. Under this embedding, we then present an optimal or nearly optimal transmission schedule for each tuning time