The Network Simplex Algorithm

For practical applications, by far the most useful optimization algorithm for solving linear programs is the celebrated simplex algorithm. With professional implementation it has a remarkable performance: problems with ?1000 variables and ?1000 restrictions can be dealt with within 0.1 to 0.5 seconds. This suggests trying to apply this algorithm also to problems from graph theory. Indeed, the most important network optimization problems may be formulated in terms of linear programs; this holds, for instance, for the determination of shortest paths, maximal flows, optimal flows, and optimal circulations.