We present a combinatorial algorithm for the 1-(S, T)-edge-connectivity augmentation problem in digraphs. The general k-(S, T)-edge-connectivity augmentation problem was first solved by A. Frank and T. Jordán, but their proof does not yield a combinatorial polynomial-time algorithm. Our algorithm generalizes an earlier result of P. Eswaran and R.E. Tarjan and relies heavily on the nature of the special case k = 1.
