A Combinatorial Multicommodity Flow Algorithm
نویسندگان
چکیده
The multicommodityow probleminvolves simultaneouslyship-ping multiplecommoditiesthrough a single network so that the total amount of ow on each edge is no more than the capacity of the edge. This problem can be expressed as a large linear program, and most known algorithms for it, both theoretical and practical, are linear programming algorithms designed to take advantage of the structure of multicommodity ow problems. The size of the linear programs, however, makes it prohibitively diicult to solve large multicommodity ow problems. In this paper, we describe and examine a multicommodity ow implementation based on the recent combinatorial approximation algorithm of Leighton et al. 13]. The theory predicts that the running time of the algorithm increases linearly with the number of commodities. Our experiments verify this behavior. The theory also predicts that the running time increases as the square of the desired precision. Our experiments show that the running time increases at most this fast, and often slower. We also compare our combinatorial implementation against two diierent linear programming-based codes. First we compare our code to that of of Kennington 10], which is a network simplex code known to perform well on multicommodity ow problems. For many problems, our combinatorial algorithm outperforms this simplex-based linear programming algorithm. More precisely, as the number of commodities increases, the running time of our algorithm grows much more slowly than that of Kennington's linear programming-based algorithm. Second, we compared our code to an interior point code of Karmarkar and Ramakrishnan. Here too, we achieved similar, but less dramatic results. Our results suggest that our algorithm may be able to solve larger multicommodity ow problems than have been solved in the past.
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تاریخ انتشار 1992