Multi-node broadcasting in all-ported 3-D wormhole-routed torus using an aggregation-then-distribution strategy

Abstract

In this paper, we investigate the multi-node broadcasting problem in a 3-D torus, where there are an unknown number of s source nodes located at unknown positions each intending to broadcast a message of size m bytes to the rest of the network. The torus is assumed to use the all-port model and the popular dimension-ordered routing. Existing congestion-free results are derived based on finding multiple edge-disjoint spanning trees in the network. This paper shows how to efficiently perform multi-node broadcasting in a 3-D torus. The main technique used in this paper is an aggregation-then-distribution strategy, which is characterized by the following features: (i) the broadcast messages are aggregated into some positions on the 3-D torus, then a number of independent subnetworks are constructed from the 3-D torus; and (ii) these subnetworks, which are responsible for distributing the messages, fully exploit the communication parallelism and the characteristic of wormhole routing. It is shown that such an approach is more appropriate than those using edge-disjoint trees for fixed-connection networks such as tori. Extensive simulations are conducted to evaluate this multi-broadcasting algorithm.