The Complexity of Interval Routing on Random Graphs

Several methods exist for routing messages in a network without using complete routing tables (compact routing). In k-interval routing schemes (k-IRS), nodes assign up to k intervals to each incident link. A message is routed over a 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 k suffice, we show that for ‘general graphs’ interval routing cannot significantly reduce the space-requirements for shortest path routing. In particular, for any δ>0, there exist classes of random graphs G n, p for all n sufficiently large such that with high probability an optimal k-IRS for a graph G ∈ G n, p requires k = Ω(n1−δ).

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