Store-and-Forward Multicast Routing on the Mesh

Abstract

We study the complexity of routing a set of messages with multiple destinations (multicast routing) on an n-node square mesh under the store-and-forward model. A standard argument proves that $\Omega(\sqrt{cn}\,)$ time is required to route n messages, where each message is generated by a distinct node and at most c messages are to be delivered to any individual node. The obvious approach of simply replicating each message into the appropriate number of unicast (single-destination) messages and routing these independently does not yield an optimal algorithm. We provide both randomized and deterministic algorithms for multicast routing, which use constant-size buffers at each node. The randomized algorithm attains optimal performance, while the deterministic algorithm is slower by a factor of O( log ² n). We also describe an optimal deterministic algorithm that, however, requires large buffers of size O(c).