Maximum Multicommodity Flow Problem with Local Requirement

The present work studies a maximum multicommodity flow problem with local constrains, which not only enrich the content of the multicommodity flow problem, but also can be used to operate optimization decisions of some practical problems, such as the logistics distribution problems stemming out of transportations. The major contributions are as follows: (A) Develop a multicommodity flow problem and study the existence of its solutions. (B) Design an approximation algorithm to solve the defined problem. (C) Propose and prove the approximation measures as well as the time complexity of the designed algorithm.