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Title page for ETD etd-042910-160853

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Author NameNahabedian, Aaron Joseph
TitleA Primal-Dual Approximation Algorithm for the Concurrent Flow Problem
DepartmentMathematical Sciences
  • William Martin, Advisor
  • Keywords
  • approximation algorithm
  • network flow
  • Date of Presentation/Defense2010-04-29
    Availability unrestricted


    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.

  • nahabedian.pdf

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