Finding disjoint paths with related path costs
 Randeep Bhatia,
 Murali Kodialam,
 T. V. Lakshman
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We consider routing in survivable networks that provide protection against node or link failures. In these networks resilience against failures is provided by routing connections on pairs of disjoint paths called primary and backup paths. The primary path of a connection carries its traffic under normal circumstances and in the eventuality of a network failure effecting the primary path the connection traffic (all or some portion of it) is rerouted over its backup path. In an online setting as connection requests arrive a pair of disjoint primary and backup paths of least total cost (under some link cost metric) are selected to route the connections. In many situations the cost metric used for the primary path differs from the cost metric used for the backup path. Also in many realistic settings these two cost metrics are related to each other.
In this paper we study the problem of finding a pair of edge or node disjoint paths of least total cost where the cost of the primary path is the total cost of its links while the cost for the backup path is α times the sum of the cost of its links, for some given α < 1. We show that the problem is hard to approximate to within a factor \(\Omega((\frac{1}{\alpha})^{1\epsilon})\) for any positive \(\epsilon \le 1\) . In addition we show that the problem is complete for a set of hard to approximate problems. On the positive side we show that a simple algorithm achieves an approximation ratio of \(O(\frac{1}{\alpha})\) for the problem.
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 Title
 Finding disjoint paths with related path costs
 Journal

Journal of Combinatorial Optimization
Volume 12, Issue 12 , pp 8396
 Cover Date
 20060901
 DOI
 10.1007/s108780068906y
 Print ISSN
 13826905
 Online ISSN
 15732886
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Industry Sectors
 Authors

 Randeep Bhatia ^{(1)}
 Murali Kodialam ^{(2)}
 T. V. Lakshman ^{(2)}
 Author Affiliations

 1. Bell Laboratories, 600 Mountain Ave, Murray Hill, NJ, 07974
 2. Bell Laboratories, 101 Crawford Corners Road, Holmdel, NJ, 07733