The.Algorithm.Design.Manual.Springer-Verlag.1998

Network Flow
Combinatorica [Ski90] provides a (slow) Mathematica implementation of network flow, with
applications to connectivity testing and matching. See Section .
Notes: The definitive book on network flows and its applications is [AMO93]. Good expositions on
preflow-push algorithms [GT88] include [CLR90]. Older augmenting path algorithms are discussed in
[Eve79a, Man89, PS82]. Expositions on min-cost flow include [Law76, PS82, SDK83]. Expositions on
the hardness of multicommodity flow [Ita78] include [Eve79a].
Conventional wisdom holds that network flow should be computable in O(nm) time, and there has been
steady progress in lowering the time complexity. See [AMO93] for a history of algorithms for the
problem. The fastest known general network flow algorithm runs in time [GT88].
Empirical studies of minimum-cost flow algorithms include [GKK74, Gol92].
Although network flow can be used to find minimum cut sets in graphs, faster algorithms are available,
including [SW94] and [MR95].
Related Problems: Linear programming (see page ), matching (see page ), connectivity (see page
).
Next: Drawing Graphs Nicely Up: Graph Problems: Polynomial-Time Previous: Edge and Vertex
Connectivity
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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