zxqfl / flow

Min cost max flow library

mcmf

This crate is for solving instances of the minimum cost maximum flow problem. It uses the network simplex algorithm from the LEMON graph optimization library.

A number of problems are special cases of min cost max flow, including max flow, single-source shortest path, and maximum weighted matching on a bipartite graph.

As such, this crate can solve all of the above problems, though it may potentially be less efficient than a specialized algorithm.

See the documentation.

Example

use mcmf::{GraphBuilder, Vertex, Cost, Capacity};
let (cost, paths) = GraphBuilder::new()
    .add_edge(Vertex::Source, "Vancouver", Capacity(2), Cost(0))
    .add_edge("Vancouver", "Toronto", Capacity(2), Cost(100))
    .add_edge("Toronto", "Halifax", Capacity(1), Cost(150))
    .add_edge("Vancouver", "Halifax", Capacity(5), Cost(400))
    .add_edge("Halifax", Vertex::Sink, Capacity(2), Cost(0))
    .mcmf();
assert_eq!(cost, 650);
assert_eq!(cost, paths.iter().map(|path| path.cost()).sum());
assert_eq!(paths.len(), 2);
assert!(
    paths[0].vertices() == vec![
        &Vertex::Source,
        &Vertex::Node("Vancouver"),
        &Vertex::Node("Halifax"),
        &Vertex::Sink]);
assert!(
    paths[1].vertices() == vec![
        &Vertex::Source,
        &Vertex::Node("Vancouver"),
        &Vertex::Node("Toronto"),
        &Vertex::Node("Halifax"),
        &Vertex::Sink]);