Reserving Resilient Capacity with Upper Bound Constraints

Continuing research begun in 2], we investigate problems of reserving capacity in the arcs of a network, subject to the constraint that, on the failure of any one arc, there is enough reserved capacity on the remaining arcs to support a ow of value T from a source s to a destination t. We also impose upper bounds on the amount of capacity we may reserve on the arcs: this alters the nature of the problem. In the case where each arc has the same upper bound, we investigate the strategy of nding the minimum-cost reservation that is itself an acyclic (s; t) ow: we show that such a reservation is easy to nd, always has a simple form, and has a cost at most twice that of the optimal solution. We investigate other related problems.