The multicommodity flow problem involves shipping multiple commodities simultaneously through a network so that the total flow over each edge does not exceed the capacity of that edge. The concurrent flow problem also associates with each commodity a demand, and involves finding the maximum fraction z, such that z of each commodity’s demand can be feasibly shipped through the network. This problem has applications in message routing, transportation, and scheduling problems. It can be formulated as a linear programming problem, and the best known solutions take advantage of decomposition techniques for linear programming. Often, quickly finding an approximate solution is more important than finding an optimal solution. A solution is epsilon-optimal if it lies within a factor of (1+epsilon) of the optimal solution. We present a combinatorial approximation algorithm for the concurrent flow problem. This algorithm consists of finding an initial flow, and gradually rerouting this flow from more to less congested paths, until an epsilon-optimal flow is achieved. This algorithm theoretically runs much faster than linear programming based algorithms.

Creator

• Nahabedian, Aaron Joseph

Contributors

• Martin, William J.

Degree

• MS

Unit

• Mathematical Sciences

Publisher

• Worcester Polytechnic Institute

Language

• English

Identifier

• etd-042910-160853

Keyword

• network flow
• approximation algorithm

Advisor

• Martin, William J.

Defense date

• 2010-04-29

Year

• 2010

Date created

• 2010-04-29

Resource type

• Report

Rights statement

• In Copyright

Last modified

• 2023-10-06