I am using the Network Simplex algorithm to solve a Maximum Flow Problem in directed graphs. In order to compare the execution time for several routing algorithms, I need to use an implementation of the simplex method by George Dantzig.
My question is : Can the Simplex Method solve a maximum flow problem in a given directed graph?
Is there any good documentation that explains the Simplex Method in graph theory?
The Network Simplex Method is a highly specialized form of the general Simplex method: it can only solve network problems.
Of course, the standard Simplex method for Linear Programming can also solve network problems, by just formulating the network problem as an LP problem.
For comparison, you may want to have a look at Cplex: it both has implementations for the (primal and dual) Simplex method for linear programming and a Network Simplex method.
Interestingly, Gurobi does not have a network Simplex method. The thought behind this is that LP solvers have become so fast that specialized network solvers have lost some of their speed advantages.
A good reference is: Ahuja, Magnanti and Orlin, Network Flows.
