Adaptive Real-Time Routing in Polynomial Time

We consider a recently-proposed problem on networks in which each individual link is characterized by two delay parameters: a (usually very conservative) guaranteed upper bound on the worst-case delay, and an estimate of the delay that is typically encountered, across the link. Given a source node, a destination node, and an upper bound on the end-to-end delay that can be tolerated, the objective is to determine routes that typically experience a small delay, while guaranteeing to respect the specified end-to-end upper bound under all circumstances. We show that the prior algorithm that has been proposed for this problem has super-polynomial running time, and derive polynomial time algorithms for solving the problem.