The Complexity of Interval Routing on Random Graphs
نویسندگان
چکیده
Several methods exist for routing messages in a network without using complete routing tables (compact routing). In k-interval routing schemes (k-IRS), links carry up to k intervals each. A message is routed over a certain link if its destination belongs to one of the intervals of the link. We present some results for the necessary value of k in order to achieve shortest-path routing. Even though low values of k suffice for very structured networks, 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 ∈ Gn,p the following holds, with high probability: if G admits an optimal k-IRS, then k = (n1− 6 ln(np) − ln(np) ln n ). The result is obtained by means of a novel matrix representation for the shortest paths in a network.
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