On devising Boolean Routing schemes

Abstract

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 considered 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 resulting from 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.

Work supported by the EEC ESPRIT II Basic Research Action Program under contract No.7141 “Algorithms and Complexity II”;, by the EEC “Human Capital and Mobility”; MAP project and by the Italian MURST 40% project “Algoritmi, Modelli di Calcolo e Strutture Informative”;.