TITLE:On the Dilation of Interval Routing AUTHORS:Cyril Gavoille ABSTRACT: In this paper we deal with interval routing on n-node networks of diameter D. We show that for every fixed D>=2, there exists a network on which every interval routing scheme with O(n/logn) intervals per link has a routing path length at least \floor{3D/2}-1. It improves the lower bound on the routing path lengths for the range of very large number of intervals. No result was known about the path lengths whenever more than \Theta(\sqrt{n}) intervals per link was used. Best-known lower bounds for a small number of intervals are 2D-O(1) for 1 interval [TL97b], and 3D/2-O(1) up to \Theta(\sqrt{n}) intervals [KRS97]. For D=2, we show a network on which any interval routing scheme using less than n/4 - o(n) intervals has a routing path of length at least 3. Moreover, we build a network of bounded degree on which every interval routing scheme with routing path lengths bounded by 3D/2 - o(D) requires \Omega(n/log^{2+e}{n}) intervals per link, where e is an arbitrary non-negative constant.