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A strongly polynomial algorithm is given for the generalized flowmaximization problem. It uses a new variant of the scaling technique, calledcontinuous scaling. The main measure of progress is that within a stronglypolynomial number of steps, an arc can be identified that must be tight inevery dual optimal solution, and thus can be contracted. As a consequence ofthe result, we also obtain a strongly polynomial algorithm for the linearfeasibility problem with at most two nonzero entries per column in theconstraint matrix.

A strongly polynomial algorithm for generalized flow maximization