Broadcasting in Butterfly and DeBruijn Networks

Broadcasting is the process of message dissemination in a communication network in which a message originated by one processor is transmitted to all processors of the network. In this paper, we present a new lower bound of 1:7417m for broadcasting in the butterry network of dimension m. This improves the best known lower bound of 1:5621m. We also describe an algorithm which improves the upper bound from 2m to 2m ? 1. This is shown to be optimal for small dimensions m. In addition, the presented lower bound technique is used to derive non-trivial lower bounds for broadcasting in the deBruijn network of dimension m. An upper bound of 1:5m+1:5 is well-known for this network. Here, we are able to improve the lower bound from 1:1374m to 1:3171m.