A New Approximation Algorithm for Computing 2-Restricted Disjoint Paths

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Chao Peng, Hong Shen

Published: 2007, Last Modified: 07 Oct 2025IEICE Trans. Inf. Syst. 2007EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: In this paper we study the problem of how to identify multiple disjoint paths that have the minimum total cost <I>OPT</I> and satisfy a delay bound <I>D</I> in a graph <I>G</I>. 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 <I>D</I> has a cost <I>OPT</I>, then our algorithm can find a solution whose delay is bounded by (1+<eq200407.gif>)<I>D</I> and the cost is no more than (1+<I>k</I>)<I>OPT</I>. The time complexity of our algorithm is much better than the previous algorithms.