Their implementations of both Dijkstra and Bellman-Ford's algorithms for finding shortest paths in graphs is SPLIB, developed by Cherkassky, Goldberg, and Radzik. They report solving instances with over one million vertices in under two minutes on a Sun Sparc-10 workstation.
Their code for finding a maximum cardinality bipartite matching of maximum weight shortest paths in graphs is CSA, developed by Goldberg and Kennedy. This code is based on a cost-scaling network flow algorithms. Their running times depend upon the density of the networks and weight distributions, but they report solving instances with over 30,000 vertices in a few minutes on a Sun Sparc-2 workstation.
Their code for solving maximum-flow in graphs is PRF, developed by Cherkassky and Goldberg. They report solving instances with over 250,000 vertices in under two minutes on a Sun Sparc-10 workstation. For minimum-cost max-flow, the higher performance code available is CS, capable of solving instances of over 30,000 vertices in a few minutes on Sun Sparc-2 workstations.
Edge and Vertex Connectivity (10) |
Network Flow (10) |
Shortest Path (10) |
Matching (9) |