Efficient Algorithms for Single Link Failure Recovery and Its Application to ATM Networks

We investigate the single link failure recovery problem and its application to the alternate path routing problem for ATM networks. Specifically, given a 2-connected graph G, a specified node s, and a shortest paths tree Ts = fe1; e2; : : : ; en 1g of s, where ei = (xi; yi) and xi = parentTs(yi), find a shortest path from yi to s in the graph Gnei for 1 i n 1. We present an O(m + n logn) time algorithm for this problem and a linear time algorithm for the case when all weights are equal. When the edge weights are integers, we present an algorithm that takes O(m+ Tsort(n)) time where Tsort(n) is the time required to sort n integers. We show that any solution to the single link recovery problem can adapted to solve the alternate path routing problem in ATM networks.