Broadcasting in WDM Optical Rings and Tori
Résumé
The well-known spanning binomial tree broadcast algorithm is generalized to obtain two families of broadcast algorithms for optical rings and two-dimensional toroidal meshes (tori) using {\em Wavelength Division Multiplexing (WDM)}. These generalizations take advantage of the concurrent transmission through optical links offered by WDM. Their performances are measured under the {\em linear cost model} : the cost of sending a message of $L$ bits is defined as $\alpha +L\tau$, where $\alpha$ is the latency and $\tau$ is the per-byte transmission cost. It is assumed that each node can concurrently transmit one message and receive one message. Our algorithms are based on the familiar spanning binomial tree and on the dimensional exchanges commonly used on hypercubes. We restrict the number of nodes in a ring and in each dimension of a torus to be a power of two. The algorithms described in this paper offer significant performance improvements over the basic spanning tree broadcast.