Boolean Routing

Abstract

In this paper, the problem of routing messages along shortest paths in a distributed network without using complete routing tables is considered. In particular, we first study the complexity of deriving minimum (in terms of number of intervals) Interval Routing schemes, proving the NP-completeness of such a problem and giving an approximation algorithm for it. Next, we propose a different routing model and show how it can be applied to improve the space requirements of representing shortest paths among all pairs of nodes for some specific network topologies. Networks considered are paths, rings, trees, hypercubes, different types of d-dimensional grids, complete graphs and complete bipartite graphs. We show that such an approach behaves strictly better than the classical Interval Routing Scheme in terms of classes of graphs which can be efficiently handled and of global knowledge mantained at each node. In particular, for all the above cases optimal representations are given. Moreover, we show that Boolean Routing is more powerful than any intervalbased routing scheme: this is done by showing that any such a scheme (on any graph) can be efficiently simulated by Boolean Routing.

Work supported by the ESPRIT II Basic Research Action Program of the European Community under contract No.7141 “Algorithms and Complexity II” and by the Italian MURST 40% project “Algoritmi, Modelli di Calcolo e Strutture Informative”.