Identifier

etd-042910-160853

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

Accessibility

Unrestricted

Subjects

approximation algorithm, network flow

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