On the dilation of interval routing

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/log n) intervals per link has a routing path length at least [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 when ever more than θ(√n) intervals per link was used. Best-known lower bounds for a small number of intervals are 2D-O(1) for 1 interval [11], and 3D/2 - O(1) up to θ(√n) intervals [5]. 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 Ω(n/log^2+ε n) intervals per link, where ε is an arbitrary non-negative constant.