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Ford Fulkerson algorithm support. (#640)
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#![feature(test)] | ||
extern crate petgraph; | ||
extern crate test; | ||
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use petgraph::algo::ford_fulkerson; | ||
use petgraph::prelude::{Graph, NodeIndex}; | ||
use test::Bencher; | ||
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#[bench] | ||
fn ford_fulkerson_bench(bench: &mut Bencher) { | ||
static NODE_COUNT: usize = 1_000; | ||
let mut g: Graph<usize, usize> = Graph::new(); | ||
let nodes: Vec<NodeIndex<_>> = (0..NODE_COUNT).map(|i| g.add_node(i)).collect(); | ||
for i in 0..NODE_COUNT - 1 { | ||
g.add_edge(nodes[i], nodes[i + 1], 1); | ||
} | ||
bench.iter(|| { | ||
let _flow = ford_fulkerson( | ||
&g, | ||
NodeIndex::from(0), | ||
NodeIndex::from(g.node_count() as u32 - 1), | ||
); | ||
}); | ||
} |
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use std::{collections::VecDeque, ops::Sub}; | ||
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use crate::{ | ||
data::DataMap, | ||
visit::{ | ||
EdgeCount, EdgeIndexable, IntoEdges, IntoEdgesDirected, NodeCount, NodeIndexable, VisitMap, | ||
Visitable, | ||
}, | ||
}; | ||
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use super::{EdgeRef, PositiveMeasure}; | ||
use crate::prelude::Direction; | ||
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fn residual_capacity<N>( | ||
network: N, | ||
edge: N::EdgeRef, | ||
vertex: N::NodeId, | ||
flow: N::EdgeWeight, | ||
) -> N::EdgeWeight | ||
where | ||
N: NodeIndexable + IntoEdges, | ||
N::EdgeWeight: Sub<Output = N::EdgeWeight> + PositiveMeasure, | ||
{ | ||
if vertex == edge.source() { | ||
// backward edge | ||
flow | ||
} else if vertex == edge.target() { | ||
// forward edge | ||
return *edge.weight() - flow; | ||
} else { | ||
let end_point = NodeIndexable::to_index(&network, vertex); | ||
panic!("Illegal endpoint {}", end_point); | ||
} | ||
} | ||
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/// Gets the other endpoint of graph edge, if any, otherwise panics. | ||
fn other_endpoint<N>(network: N, edge: N::EdgeRef, vertex: N::NodeId) -> N::NodeId | ||
where | ||
N: NodeIndexable + IntoEdges, | ||
{ | ||
if vertex == edge.source() { | ||
edge.target() | ||
} else if vertex == edge.target() { | ||
edge.source() | ||
} else { | ||
let end_point = NodeIndexable::to_index(&network, vertex); | ||
panic!("Illegal endpoint {}", end_point); | ||
} | ||
} | ||
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/// Tells whether there is an augmented path in the graph | ||
fn has_augmented_path<N>( | ||
network: N, | ||
source: N::NodeId, | ||
destination: N::NodeId, | ||
edge_to: &mut [Option<N::EdgeRef>], | ||
flows: &[N::EdgeWeight], | ||
) -> bool | ||
where | ||
N: NodeCount + IntoEdgesDirected + NodeIndexable + EdgeIndexable + Visitable, | ||
N::EdgeWeight: Sub<Output = N::EdgeWeight> + PositiveMeasure, | ||
{ | ||
let mut visited = network.visit_map(); | ||
let mut queue = VecDeque::new(); | ||
visited.visit(source); | ||
queue.push_back(source); | ||
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while let Some(vertex) = queue.pop_front() { | ||
let out_edges = network.edges_directed(vertex, Direction::Outgoing); | ||
let in_edges = network.edges_directed(vertex, Direction::Incoming); | ||
for edge in out_edges.chain(in_edges) { | ||
let next = other_endpoint(&network, edge, vertex); | ||
let edge_index: usize = EdgeIndexable::to_index(&network, edge.id()); | ||
let residual_cap = residual_capacity(&network, edge, next, flows[edge_index]); | ||
if !visited.is_visited(&next) && (residual_cap > N::EdgeWeight::zero()) { | ||
visited.visit(next); | ||
edge_to[NodeIndexable::to_index(&network, next)] = Some(edge); | ||
if destination == next { | ||
return true; | ||
} | ||
queue.push_back(next); | ||
} | ||
} | ||
} | ||
false | ||
} | ||
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fn adjust_residual_flow<N>( | ||
network: N, | ||
edge: N::EdgeRef, | ||
vertex: N::NodeId, | ||
flow: N::EdgeWeight, | ||
delta: N::EdgeWeight, | ||
) -> N::EdgeWeight | ||
where | ||
N: NodeIndexable + IntoEdges, | ||
N::EdgeWeight: Sub<Output = N::EdgeWeight> + PositiveMeasure, | ||
{ | ||
if vertex == edge.source() { | ||
// backward edge | ||
flow - delta | ||
} else if vertex == edge.target() { | ||
// forward edge | ||
flow + delta | ||
} else { | ||
let end_point = NodeIndexable::to_index(&network, vertex); | ||
panic!("Illegal endpoint {}", end_point); | ||
} | ||
} | ||
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/// \[Generic\] Ford-Fulkerson algorithm. | ||
/// | ||
/// Computes the [maximum flow][ff] of a weighted directed graph. | ||
/// | ||
/// If it terminates, it returns the maximum flow and also the computed edge flows. | ||
/// | ||
/// [ff]: https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm | ||
/// | ||
/// # Example | ||
/// ```rust | ||
/// use petgraph::Graph; | ||
/// use petgraph::algo::ford_fulkerson; | ||
/// // Example from CLRS book | ||
/// let mut graph = Graph::<u8, u8>::new(); | ||
/// let source = graph.add_node(0); | ||
/// let _ = graph.add_node(1); | ||
/// let _ = graph.add_node(2); | ||
/// let _ = graph.add_node(3); | ||
/// let _ = graph.add_node(4); | ||
/// let destination = graph.add_node(5); | ||
/// graph.extend_with_edges(&[ | ||
/// (0, 1, 16), | ||
/// (0, 2, 13), | ||
/// (1, 2, 10), | ||
/// (1, 3, 12), | ||
/// (2, 1, 4), | ||
/// (2, 4, 14), | ||
/// (3, 2, 9), | ||
/// (3, 5, 20), | ||
/// (4, 3, 7), | ||
/// (4, 5, 4), | ||
/// ]); | ||
/// let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
/// assert_eq!(23, max_flow); | ||
/// ``` | ||
pub fn ford_fulkerson<N>( | ||
network: N, | ||
source: N::NodeId, | ||
destination: N::NodeId, | ||
) -> (N::EdgeWeight, Vec<N::EdgeWeight>) | ||
where | ||
N: NodeCount | ||
+ EdgeCount | ||
+ IntoEdgesDirected | ||
+ EdgeIndexable | ||
+ NodeIndexable | ||
+ DataMap | ||
+ Visitable, | ||
N::EdgeWeight: Sub<Output = N::EdgeWeight> + PositiveMeasure, | ||
{ | ||
let mut edge_to = vec![None; network.node_count()]; | ||
let mut flows = vec![N::EdgeWeight::zero(); network.edge_count()]; | ||
let mut max_flow = N::EdgeWeight::zero(); | ||
while has_augmented_path(&network, source, destination, &mut edge_to, &flows) { | ||
let mut path_flow = N::EdgeWeight::max(); | ||
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// Find the bottleneck capacity of the path | ||
let mut vertex = destination; | ||
let mut vertex_index = NodeIndexable::to_index(&network, vertex); | ||
while let Some(edge) = edge_to[vertex_index] { | ||
let edge_index = EdgeIndexable::to_index(&network, edge.id()); | ||
let residual_capacity = residual_capacity(&network, edge, vertex, flows[edge_index]); | ||
// Minimum between the current path flow and the residual capacity. | ||
path_flow = if path_flow > residual_capacity { | ||
residual_capacity | ||
} else { | ||
path_flow | ||
}; | ||
vertex = other_endpoint(&network, edge, vertex); | ||
vertex_index = NodeIndexable::to_index(&network, vertex); | ||
} | ||
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// Update the flow of each edge along the path | ||
let mut vertex = destination; | ||
let mut vertex_index = NodeIndexable::to_index(&network, vertex); | ||
while let Some(edge) = edge_to[vertex_index] { | ||
let edge_index = EdgeIndexable::to_index(&network, edge.id()); | ||
flows[edge_index] = | ||
adjust_residual_flow(&network, edge, vertex, flows[edge_index], path_flow); | ||
vertex = other_endpoint(&network, edge, vertex); | ||
vertex_index = NodeIndexable::to_index(&network, vertex); | ||
} | ||
max_flow = max_flow + path_flow; | ||
} | ||
(max_flow, flows) | ||
} |
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use petgraph::algo::ford_fulkerson; | ||
use petgraph::prelude::Graph; | ||
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#[test] | ||
fn test_ford_fulkerson() { | ||
// Example from https://downey.io/blog/max-flow-ford-fulkerson-algorithm-explanation/ | ||
let mut graph = Graph::<usize, u16>::new(); | ||
let source = graph.add_node(0); | ||
let _ = graph.add_node(1); | ||
let _ = graph.add_node(2); | ||
let destination = graph.add_node(3); | ||
graph.extend_with_edges(&[(0, 1, 3), (0, 2, 2), (1, 2, 5), (1, 3, 2), (2, 3, 3)]); | ||
let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
assert_eq!(5, max_flow); | ||
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// Example from https://brilliant.org/wiki/ford-fulkerson-algorithm/ | ||
let mut graph = Graph::<usize, f32>::new(); | ||
let source = graph.add_node(0); | ||
let _ = graph.add_node(1); | ||
let _ = graph.add_node(2); | ||
let _ = graph.add_node(3); | ||
let _ = graph.add_node(4); | ||
let destination = graph.add_node(5); | ||
graph.extend_with_edges(&[ | ||
(0, 1, 4.), | ||
(0, 2, 3.), | ||
(1, 3, 4.), | ||
(2, 4, 6.), | ||
(3, 2, 3.), | ||
(3, 5, 2.), | ||
(4, 5, 6.), | ||
]); | ||
let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
assert_eq!(7.0, max_flow); | ||
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// Example from https://cp-algorithms.com/graph/edmonds_karp.html | ||
let mut graph = Graph::<usize, f32>::new(); | ||
let source = graph.add_node(0); | ||
let _ = graph.add_node(1); | ||
let _ = graph.add_node(2); | ||
let _ = graph.add_node(3); | ||
let _ = graph.add_node(4); | ||
let destination = graph.add_node(5); | ||
graph.extend_with_edges(&[ | ||
(0, 1, 7.), | ||
(0, 2, 4.), | ||
(1, 3, 5.), | ||
(1, 4, 3.), | ||
(2, 1, 3.), | ||
(2, 4, 2.), | ||
(3, 5, 8.), | ||
(4, 3, 3.), | ||
(4, 5, 5.), | ||
]); | ||
let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
assert_eq!(10.0, max_flow); | ||
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// Example from https://www.programiz.com/dsa/ford-fulkerson-algorithm (corrected: result not 6 but 5) | ||
let mut graph = Graph::<u8, f32>::new(); | ||
let source = graph.add_node(0); | ||
let _ = graph.add_node(1); | ||
let _ = graph.add_node(2); | ||
let _ = graph.add_node(3); | ||
let _ = graph.add_node(4); | ||
let destination = graph.add_node(5); | ||
graph.extend_with_edges(&[ | ||
(0, 1, 8.), | ||
(0, 2, 3.), | ||
(1, 3, 9.), | ||
(2, 3, 7.), | ||
(2, 4, 4.), | ||
(3, 5, 2.), | ||
(4, 5, 5.), | ||
]); | ||
let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
assert_eq!(5.0, max_flow); | ||
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let mut graph = Graph::<u8, u8>::new(); | ||
let source = graph.add_node(0); | ||
let _ = graph.add_node(1); | ||
let _ = graph.add_node(2); | ||
let _ = graph.add_node(3); | ||
let _ = graph.add_node(4); | ||
let destination = graph.add_node(5); | ||
graph.extend_with_edges(&[ | ||
(0, 1, 16), | ||
(0, 2, 13), | ||
(1, 2, 10), | ||
(1, 3, 12), | ||
(2, 1, 4), | ||
(2, 4, 14), | ||
(3, 2, 9), | ||
(3, 5, 20), | ||
(4, 3, 7), | ||
(4, 5, 4), | ||
]); | ||
let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
assert_eq!(23, max_flow); | ||
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// Example taken from https://medium.com/@jithmisha/solving-the-maximum-flow-problem-with-ford-fulkerson-method-3fccc2883dc7 | ||
let mut graph = Graph::<u8, u8>::new(); | ||
let source = graph.add_node(0); | ||
let _ = graph.add_node(1); | ||
let _ = graph.add_node(2); | ||
let _ = graph.add_node(3); | ||
let _ = graph.add_node(4); | ||
let destination = graph.add_node(5); | ||
graph.extend_with_edges(&[ | ||
(0, 1, 10), | ||
(0, 2, 10), | ||
(1, 2, 2), | ||
(1, 3, 4), | ||
(1, 4, 8), | ||
(2, 4, 9), | ||
(3, 5, 10), | ||
(4, 3, 6), | ||
(4, 5, 10), | ||
]); | ||
let (max_flow, _) = ford_fulkerson(&graph, source, destination); | ||
assert_eq!(19, max_flow); | ||
} |
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