On devising Boolean Routing Schemes

In this paper, the problem of routing messages along shortest paths in a network of processors without using complete routing tables is considered. The Boolean Routing model is proposed and it is shown that it provides optimal representations of all shortest routes on some specific network topologies (such as paths, rings, trees, hypercubes, different types of d-dimensional grids, complete graphs and complete bipartite graphs). Moreover, it is also shown that the model deals efficiently with graphs obtained by applying some types of graph compositions, thus resulting in very efficient routing schemes for some classes of networks with regular topology. This is done by considering different significant cost measures of the space efficiency of the schemes considered.