Improved Communication Schedules with Buffers

Abstract

We consider the multimessage multicasting over the n processor complete (or fully connected) static network when there are l incoming (message) buffers on every processor. We present an efficient algorithm to route the messages for every degree d problem instance in d2/l + l - 1 total communication rounds, where d is the maximum number of messages that each processor may send (or receive). Our algorithm takes linear time with respect to the input length, i.e. O(n + q) where q is the total number of messages that all processors must receive. For l = d we present a lower bound for the total communication time. The lower bound matches the upper bound for the schedules generated by our algorithm. For convenience we assume that the network is completely connected. However, it is important to note that each communication round can be automatically translated into one communication round for processors interconnected via a replication network followed by a permutation network (e.g., two adjacent Benes networks), because in these networks all possible one-to-many communications can be performed in a single communication round.