A Scaling Algorithm for Multicommodity Flow Problems

Cover A Scaling Algorithm for Multicommodity Flow Problems
A Scaling Algorithm for Multicommodity Flow Problems
Rina Schneur
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Since the parameters of real-world multicommodity problems, such as cost and capacity, are typically approximate in practice, the algorithm presented here often finds an optimal solution up to the accuracy of the data. The main component of the algorithm consists of moving flow around cycles. Thus, the algorithm focuses on cycles rather than on paths.
The efficiency of the algorithm is a result of usmg the scaling approach and of exploiting the network structure of the problem. In subsequent se
...ctions we present convergence results and prove that the algorithm has some interesting theoretical characteristics. The computational testing provides insight into the behavior of the algorithm and shows that the algorithm is quite efficient and worthy of fiirther consideration. The computational results also reveal that in some cases the theoretical bounds are observed in practice, while in other cases the bounds are much more conservative than the practical performance. The testing shows that the run time of the algorithm is competitive with the run time of recent algorithms for large scale multicommodity flow problems.

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