Simplifications and speedups of the pseudoflow algorithm

The pseudoflow algorithm for solving the maximum flow and minimum cut problems was devised in Hochbaum in [13]. The complexity of the algorithm was shown in [13] to be O(nm log n). In [5] Chandran and Hochbaum demonstrated that the pseudoflow algorithm is very efficient in practice, and that the highest label version of the algorithm tends to perform best. Here we improve the running time of the highest label pseudoflow algorithm to O(n) using simple data structures and to O(nm log(n/m)) using the dynamic trees data structure. Both these algorithms use a new form of DFS implementation that is likely to be fast in practice as well. In addition, we give a new simpler description of the pseudoflow algorithm by relating it to the simplex algorithm as applied to the maximum preflow problem defined here. The interpretation of the generic pseudoflow algorithm as a simplexlike algorithm for the maximum preflow problem motivates the pseudoflow algorithm and highlights differences between the pseudoflow algorithm and the preflow-push algorithm of Goldberg and Tarjan.