A simple method for improving the primal simplex method for the multicommodity flow problem

Abstract

We present a new efficient approach for solving the multicommodity flow problem as a sequence of subproblems, each on a very sparse but connected network. We show that each subproblem can be contracted to a problem on a much smaller graph. We then solve these problems using the simplex method. We test the algorithm on benchmark instances, and show Its improvement over the usual simplex algorithm. © 2007 Wiley Periodicals, Inc.