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releasenotes/notes/add-stoer-wagner-min-cut-algo-2211d33ba7d7f15f.yaml
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--- | ||
features: | ||
- | | ||
Added a new algorithm function, | ||
:func:`rustworkx.stoer_wagner_min_cut` that uses the | ||
Stoer Wagner algorithm for computing a weighted minimum cut | ||
in an undirected :class:`~rustworkx.PyGraph`. | ||
For example: | ||
.. jupyter-execute:: | ||
import rustworkx | ||
from rustworkx.visualization import mpl_draw | ||
graph = rustworkx.generators.grid_graph(2, 2) | ||
cut_val, partition = rustworkx.stoer_wagner_min_cut(graph) | ||
colors = [ | ||
'orange' if node in partition else 'blue' for node in graph.node_indexes() | ||
] | ||
mpl_draw(graph, node_color=colors) |
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// Licensed under the Apache License, Version 2.0 (the "License"); you may | ||
// not use this file except in compliance with the License. You may obtain | ||
// a copy of the License at | ||
// | ||
// http://www.apache.org/licenses/LICENSE-2.0 | ||
// | ||
// Unless required by applicable law or agreed to in writing, software | ||
// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT | ||
// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the | ||
// License for the specific language governing permissions and limitations | ||
// under the License. | ||
|
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use hashbrown::HashMap; | ||
use num_traits::Zero; | ||
use std::{hash::Hash, ops::AddAssign}; | ||
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use priority_queue::PriorityQueue; | ||
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use petgraph::{ | ||
stable_graph::StableUnGraph, | ||
visit::{Bfs, EdgeCount, EdgeRef, GraphProp, IntoEdges, IntoNodeIdentifiers, NodeCount}, | ||
Undirected, | ||
}; | ||
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type StCut<K, T> = Option<((T, T), K)>; | ||
type MinCut<K, T, E> = Result<Option<(K, Vec<T>)>, E>; | ||
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fn zip<T, U>(a: Option<T>, b: Option<U>) -> Option<(T, U)> { | ||
match (a, b) { | ||
(Some(a), Some(b)) => Some((a, b)), | ||
_ => None, | ||
} | ||
} | ||
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fn stoer_wagner_phase<G, F, K>(graph: G, mut edge_cost: F) -> StCut<K, G::NodeId> | ||
where | ||
G: GraphProp<EdgeType = Undirected> + IntoEdges + IntoNodeIdentifiers, | ||
G::NodeId: Hash + Eq, | ||
F: FnMut(G::EdgeRef) -> K, | ||
K: Copy + Ord + Zero + AddAssign, | ||
{ | ||
let mut pq = PriorityQueue::<G::NodeId, K, ahash::RandomState>::from( | ||
graph | ||
.node_identifiers() | ||
.map(|nx| (nx, K::zero())) | ||
.collect::<Vec<(G::NodeId, K)>>(), | ||
); | ||
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let mut cut_w = None; | ||
let (mut s, mut t) = (None, None); | ||
while let Some((nx, nx_val)) = pq.pop() { | ||
s = t; | ||
t = Some(nx); | ||
cut_w = Some(nx_val); | ||
for edge in graph.edges(nx) { | ||
pq.change_priority_by(&edge.target(), |x| { | ||
*x += edge_cost(edge); | ||
}) | ||
} | ||
} | ||
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zip(zip(s, t), cut_w) | ||
} | ||
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/// Stoer-Wagner's min cut algorithm. | ||
/// | ||
/// Compute a weighted minimum cut using the Stoer-Wagner algorithm [`stoer_simple_1997`](https://dl.acm.org/doi/10.1145/263867.263872). | ||
/// | ||
/// The graph should be undirected. If the input graph is disconnected, | ||
/// a cut with zero value will be returned. For graphs with less than | ||
/// two nodes, this function returns [`None`]. The function `edge_cost` | ||
/// should return the cost for a particular edge. Edge costs must be non-negative. | ||
/// | ||
/// Returns a tuple containing the value of a minimum cut and a vector | ||
/// of all `NodeId`s contained in one part of the partition that defines a minimum cut. | ||
/// | ||
/// # Example | ||
/// ```rust | ||
/// use std::collections::HashSet; | ||
/// use std::iter::FromIterator; | ||
/// | ||
/// use rustworkx_core::connectivity::stoer_wagner_min_cut; | ||
/// use rustworkx_core::petgraph::graph::{NodeIndex, UnGraph}; | ||
/// use rustworkx_core::Result; | ||
/// | ||
/// let mut graph : UnGraph<(), ()> = UnGraph::new_undirected(); | ||
/// let a = graph.add_node(()); // node with no weight | ||
/// let b = graph.add_node(()); | ||
/// let c = graph.add_node(()); | ||
/// let d = graph.add_node(()); | ||
/// let e = graph.add_node(()); | ||
/// let f = graph.add_node(()); | ||
/// let g = graph.add_node(()); | ||
/// let h = graph.add_node(()); | ||
/// | ||
/// graph.extend_with_edges(&[ | ||
/// (a, b), | ||
/// (b, c), | ||
/// (c, d), | ||
/// (d, a), | ||
/// (e, f), | ||
/// (b, e), | ||
/// (f, g), | ||
/// (g, h), | ||
/// (h, e) | ||
/// ]); | ||
/// // a ---- b ---- e ---- f | ||
/// // | | | | | ||
/// // d ---- c h ---- g | ||
/// | ||
/// let min_cut_res: Result<Option<(usize, Vec<_>)>> = | ||
/// stoer_wagner_min_cut(&graph, |_| Ok(1)); | ||
/// | ||
/// let (min_cut, partition) = min_cut_res.unwrap().unwrap(); | ||
/// assert_eq!(min_cut, 1); | ||
/// assert_eq!( | ||
/// HashSet::<NodeIndex>::from_iter(partition), | ||
/// HashSet::from_iter([e, f, g, h]) | ||
/// ); | ||
/// ``` | ||
pub fn stoer_wagner_min_cut<G, F, K, E>(graph: G, mut edge_cost: F) -> MinCut<K, G::NodeId, E> | ||
where | ||
G: GraphProp<EdgeType = Undirected> + IntoEdges + IntoNodeIdentifiers + NodeCount + EdgeCount, | ||
G::NodeId: Hash + Eq, | ||
F: FnMut(G::EdgeRef) -> Result<K, E>, | ||
K: Copy + Ord + Zero + AddAssign, | ||
{ | ||
let mut graph_with_super_nodes = | ||
StableUnGraph::with_capacity(graph.node_count(), graph.edge_count()); | ||
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let mut node_map = HashMap::with_capacity(graph.node_count()); | ||
let mut rev_node_map = HashMap::with_capacity(graph.node_count()); | ||
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for node in graph.node_identifiers() { | ||
let index = graph_with_super_nodes.add_node(()); | ||
node_map.insert(node, index); | ||
rev_node_map.insert(index, node); | ||
} | ||
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for edge in graph.edge_references() { | ||
let cost = edge_cost(edge)?; | ||
let source = node_map[&edge.source()]; | ||
let target = node_map[&edge.target()]; | ||
graph_with_super_nodes.add_edge(source, target, cost); | ||
} | ||
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if graph_with_super_nodes.node_count() == 0 { | ||
return Ok(None); | ||
} | ||
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let (mut best_phase, mut min_cut_val) = (None, None); | ||
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let mut contractions = Vec::new(); | ||
for phase in 0..(graph_with_super_nodes.node_count() - 1) { | ||
if let Some(((s, t), cut_w)) = | ||
stoer_wagner_phase(&graph_with_super_nodes, |edge| *edge.weight()) | ||
{ | ||
if min_cut_val.is_none() || Some(cut_w) < min_cut_val { | ||
best_phase = Some(phase); | ||
min_cut_val = Some(cut_w); | ||
} | ||
// now merge nodes ``s`` and ``t``. | ||
contractions.push((s, t)); | ||
let edges = graph_with_super_nodes | ||
.edges(t) | ||
.map(|edge| (s, edge.target(), *edge.weight())) | ||
.collect::<Vec<_>>(); | ||
for (source, target, cost) in edges { | ||
if let Some(edge_index) = graph_with_super_nodes.find_edge(source, target) { | ||
graph_with_super_nodes[edge_index] += cost; | ||
} else { | ||
graph_with_super_nodes.add_edge(source, target, cost); | ||
} | ||
} | ||
graph_with_super_nodes.remove_node(t); | ||
} | ||
} | ||
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// Recover the optimal partitioning from the contractions | ||
let min_cut = best_phase.map(|phase| { | ||
let mut clustered_graph = StableUnGraph::<(), ()>::default(); | ||
clustered_graph.extend_with_edges(&contractions[..phase]); | ||
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let node = contractions[phase].1; | ||
if clustered_graph.contains_node(node) { | ||
let mut cluster = Vec::new(); | ||
let mut bfs = Bfs::new(&clustered_graph, node); | ||
while let Some(nx) = bfs.next(&clustered_graph) { | ||
cluster.push(rev_node_map[&nx]) | ||
} | ||
cluster | ||
} else { | ||
vec![rev_node_map[&node]] | ||
} | ||
}); | ||
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Ok(zip(min_cut_val, min_cut)) | ||
} |
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