Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM9804March 1998 
G. Brightwell, G. Oriolo, and F.B. Shepherd
Abstract
We examine various problems concerning the reservation of nonshared capacity for traffic in a network between sourcedestination pairs so as to be ``resilient'' against one or more network failures. In the simplest version of the problem we consider, the resilience requirement is that for a pair (s,t), on the failure of any one arc of the network, there is sufficient reserved capacity in the remainder of the network to support an (s,t) flow of some given value T. The most striking results come in the case where the reservation has to consist of a collection of arcdisjoint paths. Here we give a very simple algorithm to find a minimum cost fractional solution, based on finding minimum cost network flows. Unlike traditional network flow problems, however, the integral version does not come for free: we do however give a polynomial time 1/14approximation algorithm, and show that this is best possible. These algorithms can also be adapted to solve other versions, for instance in an acyclic network when the reserved capacity has to constitute an integer flow. We leave many problems open, and provide a number of examples.
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