An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow

Theminimum-cost multicommodity ow problem involves simultaneously shipping multiple commodities through a single network so that the total ow obeys arc capacity constraints and has minimum cost. Multicommodity ow problems can be expressed as linear programs, and most theoretical and practical algorithms use linear-programming algorithms specialized for the problems' structures. Combinatorial approximation algorithms in [GK95, KP95b, PST95] yield ows with costs slightly larger than the minimum cost and use capacities slightly larger than the given capacities. Theoretically, the running times of these algorithms are much less than that of linear-programming-based algorithms. We combine and modify the theoretical ideas in these approximation algorithms to yield a fast, practical implementation solving the minimumcost multicommodity ow problem. Experimentally, the algorithm solved our problem instances (to 1% accuracy) two to three orders of magnitude faster than the linear-programming package CPLEX [CPL95] and the linearprogramming based multicommodity ow program PPRN [CN96].