Augmenting graphs to meet edge-connectivity requirements

The problem of determining the minimum number gamma of edges to be added to a graph G so that in the resulting graph the edge-connectivity between every pair (u,v) of nodes is at least a prescribed value r(u,v) is treated. A min-max formula for gamma is derived, and a polynomial-time algorithm for computing gamma is described. The directed counterpart of the problem is also solved for the case in which r(u,v)=k>or=1. The approach used makes it possible to solve a degree-constrained version of the problem. The minimum-cost augmentation problem can also be solved in polynomial time provided that the edge costs arise from node costs.<
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