Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-2000-03 March 2000

Abstract

Continuing research begun in an earlier paper, 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 flow 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 finding the minimum-cost reservation that is itself an acyclic  (s,t)  flow: we show that such a reservation is easy to find, always has a simple form, and has a cost at most twice that of the optimal solution.
We investigate other related problems.

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