Resilient and low stretch routing through embedding into tree metrics

Abstract

Given a network, the simplest routing scheme is probably routing on a spanning tree. This method however does not provide good stretch - the route between two nodes can be much longer than their shortest distance, nor does it give good resilience - one node failure may disconnect quadratically many pairs. In this paper we use two trees to achieve both constant stretch and good resilience. Given a metric (e.g., as the shortest path metric of a given communication network), we build two hierarchical well-separated trees using randomization such that for any two nodes u, v, the shorter path of the two paths in the two respective trees gives a constant stretch of the metric distance of u, v, and the removal of any node only disconnect the routes between O(1/n) fraction of all pairs. Both bounds are in expectation and hold true as long as the metric follows certain geometric growth rate (the number of nodes within distance r is a polynomial function of r), which holds for many realistic network settings such as wireless ad hoc networks and Internet backbone graphs. The algorithms have been implemented and tested on real data. © 2011 Springer-Verlag.