Implementation of a combinatorial multicommodity flow algorithm
Tishya Leong, Peter W. Shor, Clifford Stein · DIMACS series in discrete mathematics and theoretical computer science · 1993
The multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total amount of flow 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 flow problems. The size of the linear programs, however, makes it prohibitively difficult to solve large multicommodity flow problems. In this paper, we describe and examine a multicommodity flow 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 ...