Extended maximum concurrent flow problem with saturated capacity

TL;DR

This paper introduces an extended maximum concurrent flow problem with saturated capacity, proves solution existence, and develops an approximation algorithm with analyzed complexity and performance guarantees.

Contribution

It defines a new variant of the flow problem, proves solution existence, and provides an approximation algorithm with complexity and approximation bounds.

Findings

Solution existence is proven.

An approximation algorithm is designed.

Algorithm complexity and approximation ratio are analyzed.

Abstract

The present work studies a kind of Maximum Concurrent Flow Problem, called as Extended Maximum Concurrent Flow Problem with Saturated Capacity. Our major contributions are as follows: (A) Propose the definition of Extensive Maximum Concurrent Flow Problem with Saturated Capacity and prove its solutions exist. (B) Design a approximation algorithm to solve the problem. (C) Propose and prove the complexity and the approximation measures of the algorithm we design.