On the Dilation of Interval Routing

In this paper we deal with interval routing on n-node networks of diameter D. We show that, for all n and D such that 2 ≤ D ≤ 2(n), there exists a network on which every interval routing scheme with less than (n/(D log(n/D))) intervals per link has a routing path length at least b3D/2c − 1. It improves the lower bound on the routing path lengths for the range of a very large number of intervals. Moreover, we build a network of bounded degree, for all n and D such that 2(log n) ≤ D ≤ 2(n), on which every interval routing scheme with less than (n/D2) intervals per link has a routing path length at least 3D/2 − O(log n).