Augmenting Capacities in Networks
نویسنده
چکیده
Consider a network N = (V; E; c) with an integer valued capacity function c: V V ! Z + , and let k be a positive integer. What is the minimal total increase by which the individual capacities must be increased in order that the value of the maximal ow between all nodes is at least k? Frank FRANK92] gives a min-max formula for which is proved using Maders MADER82] splitting theorem. In order to obtain an eecient implementation of the resulting polynomial time algorithm, one must carry out some reduction and splitting operations which, in turn, entail performing several maximal ow computations. We give a method for reducing the total number of maximalow computations which signiicantly decreases the time complexity of the reduction phase, and substantially reduces the running time of the entire algorithm.
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