Scaling implementation of the tension rectification algorithm to solve the feasible differential problem

The feasible differential problem is solved using a tension rectification algorithm. in this paper, we present a scaling implementation of a tension rectification algorithm. let n; m; u denote the number of nodes, number of arcs, and maximum arc capacity value of an arc, respectively. our implementation runs in o(mnlog u), which is o(mnlog n) under the similarity assumption. the tension rectification algorithm runs in o(m^2) time, so, our implementation is an improvement if n log n < m. another merit of our algorithm is that, in cases where the feasible differential problem does not have a solution, it presents some information that is useful to the modeler in estimating the maximum cost of adjusting the network.