A New Approximation Algorithm for Computing 2-Restricted Disjoint Paths

Chao PENG  Hong SHEN  

IEICE TRANSACTIONS on Information and Systems   Vol.E90-D   No.2   pp.465-472
Publication Date: 2007/02/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.2.465
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Algorithm Theory
approximation algorithms,  fault-tolerant routing,  disjoint paths,  Lagrangian Relaxation,  

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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+)D and the cost is no more than (1+k)OPT. The time complexity of our algorithm is much better than the previous algorithms.