The last two sections address optimization problems modeled on network structures, particularly the shortest path problem and the

maximum flow problem, and discrete optimization problems where the variables are constrained to take integer values.

The maximum flow problem and its dual, the minimum cut problem, are classical combinatorial problems with a wide variety of scientific and engineering applications.

The network simplex method of Dantzig [1951] for the transportation problem solves the maximum flow problem as a natural special case.

Most efficient algorithms for the maximum flow problem are based on the blocking flow and the push-relabel methods.

The maximum flow problem can be solved in O([Lambda]m log([n.

The maximum flow problem can be solved in O([Lambda]n log(n) log U) time on a PRAM with O([n.

A fast and simple algorithm for the maximum flow problem.