problemreductions/models/graph/
maximum_matching.rs

1//! MaximumMatching problem implementation.
2//!
3//! The Maximum Matching problem asks for a maximum weight set of edges
4//! such that no two edges share a vertex.
5
6use crate::registry::{CreateSpec, ProblemSchemaEntry, VariantDimension};
7use crate::topology::{Graph, SimpleGraph};
8use crate::traits::Problem;
9use crate::types::{Max, WeightElement};
10use num_traits::Zero;
11use serde::{Deserialize, Serialize};
12use std::collections::HashMap;
13
14inventory::submit! {
15    ProblemSchemaEntry {
16        name: "MaximumMatching",
17        display_name: "Maximum Matching",
18        aliases: &["MaxMatching"],
19        dimensions: &[
20            VariantDimension::new("graph", "SimpleGraph", &["SimpleGraph"]),
21            VariantDimension::new("weight", "i64", &["i64"]),
22        ],
23        category: crate::registry::ProblemCategory::Graph,
24        module_path: module_path!(),
25        description: "Find maximum weight matching in a graph",
26        fields: MaximumMatchingCreateSpec::FIELDS,
27    }
28}
29
30/// The Maximum Matching problem.
31///
32/// Given a graph G = (V, E) with edge weights, find a maximum weight
33/// subset M ⊆ E such that no two edges in M share a vertex.
34///
35/// # Type Parameters
36///
37/// * `G` - The graph type (e.g., `SimpleGraph`, `KingsSubgraph`, `UnitDiskGraph`)
38/// * `W` - The weight type (e.g., `i64`, `f64`, `One`)
39///
40/// # Example
41///
42/// ```
43/// use problemreductions::models::graph::MaximumMatching;
44/// use problemreductions::topology::SimpleGraph;
45/// use problemreductions::{Problem, BruteForce};
46///
47/// // Path graph 0-1-2
48/// let graph = SimpleGraph::new(3, vec![(0, 1), (1, 2)]);
49/// let problem = MaximumMatching::<_, i64>::unit_weights(graph);
50///
51/// let solver = BruteForce::new();
52/// let solutions = solver.find_all_witnesses(&problem).unwrap();
53///
54/// // Maximum matching has 1 edge
55/// for sol in &solutions {
56///     assert_eq!(sol.iter().filter(|&&selected| selected).count(), 1);
57/// }
58/// ```
59#[derive(Debug, Clone, Serialize, Deserialize)]
60pub struct MaximumMatching<G, W> {
61    /// The underlying graph.
62    graph: G,
63    /// Weights for each edge (in edge index order).
64    edge_weights: Vec<W>,
65}
66
67#[derive(Debug, Deserialize, crate::CreateSpec)]
68struct MaximumMatchingCreateSpec {
69    #[create(codec = "edge-list")]
70    graph: Vec<(usize, usize)>,
71    num_vertices: Option<usize>,
72    #[create(codec = "comma-separated")]
73    edge_weights: Option<Vec<i64>>,
74}
75
76impl TryFrom<MaximumMatchingCreateSpec> for MaximumMatching<SimpleGraph, i64> {
77    type Error = crate::registry::ConstructionError;
78
79    fn try_from(spec: MaximumMatchingCreateSpec) -> Result<Self, Self::Error> {
80        let graph = simple_graph_from_create(spec.graph, spec.num_vertices)?;
81        let edge_weights = spec
82            .edge_weights
83            .unwrap_or_else(|| vec![1; graph.num_edges()]);
84        if edge_weights.len() != graph.num_edges() {
85            return Err(format!(
86                "edge_weights has length {}, expected {}",
87                edge_weights.len(),
88                graph.num_edges()
89            )
90            .into());
91        }
92        Ok(Self::new(graph, edge_weights))
93    }
94}
95
96fn simple_graph_from_create(
97    edges: Vec<(usize, usize)>,
98    num_vertices: Option<usize>,
99) -> Result<SimpleGraph, crate::registry::ConstructionError> {
100    if edges.is_empty() && num_vertices.is_none() {
101        return Err("num_vertices is required for an empty graph"
102            .to_string()
103            .into());
104    }
105    for (index, &(u, v)) in edges.iter().enumerate() {
106        if u == v {
107            return Err(format!("graph edge {index} is a self-loop at vertex {u}").into());
108        }
109    }
110    let inferred = edges
111        .iter()
112        .flat_map(|&(u, v)| [u, v])
113        .max()
114        .map(|vertex| vertex.checked_add(1).ok_or("vertex count overflows usize"))
115        .transpose()?
116        .unwrap_or(0);
117    let num_vertices = num_vertices.unwrap_or(inferred);
118    if num_vertices < inferred {
119        return Err(format!(
120            "num_vertices {num_vertices} is too small for graph endpoints; need at least {inferred}"
121        )
122        .into());
123    }
124    Ok(SimpleGraph::new(num_vertices, edges))
125}
126
127impl<G: Graph, W: Clone + Default> MaximumMatching<G, W> {
128    /// Create a MaximumMatching problem from a graph with given edge weights.
129    ///
130    /// # Arguments
131    /// * `graph` - The graph
132    /// * `edge_weights` - Weight for each edge (in graph.edges() order)
133    pub fn new(graph: G, edge_weights: Vec<W>) -> Self {
134        assert_eq!(
135            edge_weights.len(),
136            graph.num_edges(),
137            "edge_weights length must match num_edges"
138        );
139        Self {
140            graph,
141            edge_weights,
142        }
143    }
144
145    /// Create a MaximumMatching problem with unit weights.
146    pub fn unit_weights(graph: G) -> Self
147    where
148        W: WeightElement,
149    {
150        let edge_weights = vec![W::unit(); graph.num_edges()];
151        Self {
152            graph,
153            edge_weights,
154        }
155    }
156
157    /// Get a reference to the underlying graph.
158    pub fn graph(&self) -> &G {
159        &self.graph
160    }
161
162    /// Get edge endpoints.
163    pub fn edge_endpoints(&self, edge_idx: usize) -> Option<(usize, usize)> {
164        self.graph.edges().get(edge_idx).copied()
165    }
166
167    /// Get all edges with their endpoints and weights.
168    pub fn edges(&self) -> Vec<(usize, usize, W)> {
169        self.graph
170            .edges()
171            .into_iter()
172            .zip(self.edge_weights.iter().cloned())
173            .map(|((u, v), w)| (u, v, w))
174            .collect()
175    }
176
177    /// Build a map from vertices to incident edges.
178    pub fn vertex_to_edges(&self) -> HashMap<usize, Vec<usize>> {
179        let mut v2e: HashMap<usize, Vec<usize>> = HashMap::new();
180        for (idx, (u, v)) in self.graph.edges().iter().enumerate() {
181            v2e.entry(*u).or_default().push(idx);
182            v2e.entry(*v).or_default().push(idx);
183        }
184        v2e
185    }
186
187    /// Check if a configuration is a valid matching.
188    pub fn is_valid_solution(&self, config: &[bool]) -> bool {
189        self.is_valid_matching(config)
190    }
191
192    /// Check if a configuration is a valid matching (internal).
193    fn is_valid_matching(&self, config: &[bool]) -> bool {
194        let mut vertex_used = vec![false; self.graph.num_vertices()];
195
196        for (idx, &selected) in config.iter().enumerate() {
197            if selected {
198                if let Some((u, v)) = self.edge_endpoints(idx) {
199                    if vertex_used[u] || vertex_used[v] {
200                        return false;
201                    }
202                    vertex_used[u] = true;
203                    vertex_used[v] = true;
204                }
205            }
206        }
207        true
208    }
209
210    /// Set new weights for the problem.
211    pub fn set_weights(&mut self, weights: Vec<W>) {
212        assert_eq!(weights.len(), self.graph.num_edges());
213        self.edge_weights = weights;
214    }
215
216    /// Get the weights for the problem.
217    pub fn weights(&self) -> Vec<W> {
218        self.edge_weights.clone()
219    }
220
221    /// Check if the problem uses a non-unit weight type.
222    pub fn is_weighted(&self) -> bool
223    where
224        W: WeightElement,
225    {
226        !W::IS_UNIT
227    }
228}
229
230impl<G: Graph, W: WeightElement> MaximumMatching<G, W> {
231    /// Get the number of vertices in the underlying graph.
232    pub fn num_vertices(&self) -> usize {
233        self.graph().num_vertices()
234    }
235
236    /// Get the number of edges in the underlying graph.
237    pub fn num_edges(&self) -> usize {
238        self.graph().num_edges()
239    }
240}
241
242impl<G, W> Problem for MaximumMatching<G, W>
243where
244    G: Graph + crate::variant::VariantParam,
245    W: WeightElement + crate::variant::VariantParam,
246{
247    const NAME: &'static str = "MaximumMatching";
248    type Solution = Vec<bool>;
249    type Value = Max<W::Sum>;
250
251    crate::problem_parameters![("num_edges", num_edges), ("num_vertices", num_vertices),];
252
253    fn variant() -> Vec<(&'static str, &'static str)> {
254        crate::variant_params![G, W]
255    }
256
257    fn evaluate(
258        &self,
259        config: &Self::Solution,
260    ) -> Result<Max<W::Sum>, crate::traits::EvaluationError> {
261        if config.len() != self.graph.num_edges() {
262            return Err(crate::traits::EvaluationError::InvalidConfiguration(
263                "edge-selection length does not match the graph".into(),
264            ));
265        }
266        Ok({
267            if !self.is_valid_matching(config) {
268                return Ok(Max(None));
269            }
270            let mut total = W::Sum::zero();
271            for (idx, &selected) in config.iter().enumerate() {
272                if selected {
273                    if let Some(w) = self.edge_weights.get(idx) {
274                        total = W::checked_add_to_sum(
275                            total,
276                            w.to_sum(),
277                            "summing selected matching-edge weights",
278                        )?;
279                    }
280                }
281            }
282            Max(Some(total))
283        })
284    }
285}
286
287impl<G, W> crate::solvers::BruteForceProblem for MaximumMatching<G, W>
288where
289    G: Graph + crate::variant::VariantParam,
290    W: WeightElement + crate::variant::VariantParam,
291{
292    fn dimensions(&self) -> Vec<usize> {
293        vec![2; self.graph.num_edges()]
294    }
295}
296
297crate::impl_random_generate!(MaximumMatching<SimpleGraph, i64>, crate::random::SimpleGraphRandomSpec, |spec| {
298    let graph = spec.graph()?;
299    let weights = vec![1; graph.num_edges()];
300    Ok(MaximumMatching::new(graph, weights))
301});
302
303crate::declare_variants! {
304    default MaximumMatching<SimpleGraph, i64> => "num_vertices^3" create MaximumMatchingCreateSpec random,
305}
306
307crate::register_brute_force! {
308    MaximumMatching<SimpleGraph, i64> decode |_, indices: Vec<usize>| crate::config::config_to_bits(&indices),
309}
310
311#[cfg(feature = "example-db")]
312pub(crate) fn canonical_model_example_specs() -> Vec<crate::example_db::specs::ModelExampleSpec> {
313    vec![crate::example_db::specs::ModelExampleSpec {
314        id: "maximum_matching_simplegraph",
315        instance: Box::new(MaximumMatching::<_, i64>::unit_weights(SimpleGraph::new(
316            5,
317            vec![(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (3, 4)],
318        ))),
319        optimal_config: serde_json::json!(vec![true, false, false, false, true, false]),
320        optimal_value: serde_json::json!(2),
321    }]
322}
323
324/// Check if a selection of edges forms a valid matching.
325///
326/// # Panics
327/// Panics if `selected.len() != graph.num_edges()`.
328#[cfg(test)]
329pub(crate) fn is_matching<G: Graph>(graph: &G, selected: &[bool]) -> bool {
330    assert_eq!(
331        selected.len(),
332        graph.num_edges(),
333        "selected length must match num_edges"
334    );
335
336    let edges = graph.edges();
337    let mut vertex_used = vec![false; graph.num_vertices()];
338    for (idx, &sel) in selected.iter().enumerate() {
339        if sel {
340            let (u, v) = edges[idx];
341            if vertex_used[u] || vertex_used[v] {
342                return false;
343            }
344            vertex_used[u] = true;
345            vertex_used[v] = true;
346        }
347    }
348    true
349}
350
351#[cfg(test)]
352#[path = "../../unit_tests/models/graph/maximum_matching.rs"]
353mod tests;
problemreductions/models/graph/maximum_matching.rs

problemreductions/models/graph/
maximum_matching.rs
