A New Approximation Algorithm for Computing 2-Restricted Disjoint Paths

In this paper we study the problem of how to identify multiple disjoint paths that have the minimum total cost OPT and satisfy a delay bound D in a graph G. This problem has lots of applications in networking such as fault-tolerant quality of service (QoS) routing and network-flow load balancing. Recently, several approximation algorithms have been developed for this problem. Here, we propose a new approximation algorithm for it by using the Lagrangian Relaxation method. We then present a simple approximation algorithm for finding multiple link-disjoint paths that satisfy the delay constraints at a reasonable total cost. If the optimal solution under delay-bound D has a cost OPT , then our algorithm can find a solution whose delay is bounded by (1+ 1 k )D and the cost is no more than (1+k)OPT . The time complexity of our algorithm is much better than the previous algorithms. key words: Approximation Algorithms, Fault-Tolerant Routing, Disjoint Paths, Lagrangian Relaxation