Compact Routing Schemes with Improved Stretch

We consider the problem of compact routing in weighted general undirected graphs, in which the goal is to construct local routing tables that allow information to be sent on short paths in the network. In this paper the first improvement to the work of Thorup and Zwick [SPAA’01] is presented. Specifically, we construct an improved routing scheme obtaining for every k routing tables of size ˜O(n^1/k log D), and stretch (4-α)k-β for some absolute constants α,β > 0, where D is the normalized diameter. This provides a positive answer to a main open question in this area as to the existence of a routing scheme with stretch ck for some constant c<4.