#### Faculty Advisor

William Martin

#### Abstract

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.

#### Publisher

Worcester Polytechnic Institute

#### Degree Name

MS

#### Department

Mathematical Sciences

#### Project Type

Thesis

#### Date Accepted

2010-04-29

#### Copyright Statement

All authors have granted to WPI a nonexclusive royalty-free license to distribute copies of the work. Copyright is held by the author or authors, with all rights reserved, unless otherwise noted. If you have any questions, please contact wpi-etd@wpi.edu.

#### Accessibility

Unrestricted

#### Repository Citation

Nahabedian, Aaron Joseph, "A Primal-Dual Approximation Algorithm for the Concurrent Flow Problem" (2010). *Masters Theses (All Theses, All Years)*. 474.

https://digitalcommons.wpi.edu/etd-theses/474

#### Subjects

approximation algorithm, network flow