International Academy of Ecology and Environmental Sciences
Network Biology
2220-8879
11
2
2021
6
1
A bit-capacity scaling algorithm for the constrained minimal cost
network flow problem
82-96
EN
Muhammad Tlas
http://www.iaees.org/publications/journals/nb/articles/2021-11(2)/constrained-minimal-cost-network-flow-problem.pdf>
A polynomial time algorithm for solving the minimum-cost network flow problem has been proposed in this paper. This algorithm is mainly based on the binary representation of capacities; it solves the minimum-cost flow problem in directed graph of n nodes and m directed arcs as a sequence of O(n2) shortest path problems on residual networks. The algorithm runs in O(n2mr) time, where r is the smallest integer greater than or equal to Log2B, and B is the largest arc capacity of the network. A generalization of this proposed algorithm has been also performed in order to solve the minimum-cost flow problem in a directed network subject to non-negative lower bound on the flow vector. A formulation of both the transportation and the assignment problems, as a minimal cost network flow problem has been also performed. A numerical example has been inserted to illustrate the use of the proposed method.