Abstract

Several methods exist for routing messages in a network without using complete routing tables (compact routing). In k-interval routing schemes (k-IR.S), links carry up to k intervals each. A message is routed over certain link if its destination belongs to one of the intervals of the link. We give some results for the necessary value of k in order to achieve shortest path routing. Even though for very structured networks low values of suce, we show that for 'general graphs' interval routing cannot significantly reduce the space-requirements for shortest path routing. In particular we show that for suitably large n, there are suitable values of p such that for randomly chosen graphs G 6 ,p the following holds, with high probability: if G admits an optimal k-IIS, then k = The result is obtained by means of a novel matrix representation for the shortest paths in a network.

Citations