A approximation algorithm to solve the maximum multicommodity flow problem with local dominant

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) A multicommodity flow problem is developed and the existence of its solutions is studied. (B) An approximation algorithm to solve the defined problem is designed. (C) The approximation measures as well as the time complexity of the designed algorithm is proposed and proved.