problemreductions/models/graph/

maximum_clique.rs

//! MaximumClique problem implementation.
//!
//! The MaximumClique problem asks for a maximum weight subset of vertices
//! such that all vertices in the subset are pairwise adjacent.

use crate::registry::{FieldInfo, ProblemSchemaEntry};
use crate::topology::{Graph, SimpleGraph};
use crate::traits::{OptimizationProblem, Problem};
use crate::types::{Direction, SolutionSize, WeightElement};
use num_traits::Zero;
use serde::{Deserialize, Serialize};

inventory::submit! {
    ProblemSchemaEntry {
        name: "MaximumClique",
        module_path: module_path!(),
        description: "Find maximum weight clique in a graph",
        fields: &[
            FieldInfo { name: "graph", type_name: "G", description: "The underlying graph G=(V,E)" },
            FieldInfo { name: "weights", type_name: "Vec<W>", description: "Vertex weights w: V -> R" },
        ],
    }
}

/// The MaximumClique problem.
///
/// Given a graph G = (V, E) and weights w_v for each vertex,
/// find a subset S ⊆ V such that:
/// - All vertices in S are pairwise adjacent (clique constraint)
/// - The total weight Σ_{v ∈ S} w_v is maximized
///
/// # Type Parameters
///
/// * `G` - The graph type (e.g., `SimpleGraph`, `KingsSubgraph`, `UnitDiskGraph`)
/// * `W` - The weight type (e.g., `i32`, `f64`, `One`)
///
/// # Example
///
/// ```
/// use problemreductions::models::graph::MaximumClique;
/// use problemreductions::topology::SimpleGraph;
/// use problemreductions::{Problem, Solver, BruteForce};
///
/// // Create a triangle graph (3 vertices, 3 edges - complete graph)
/// let graph = SimpleGraph::new(3, vec![(0, 1), (1, 2), (0, 2)]);
/// let problem = MaximumClique::new(graph, vec![1; 3]);
///
/// // Solve with brute force
/// let solver = BruteForce::new();
/// let solutions = solver.find_all_best(&problem);
///
/// // Maximum clique in a triangle (K3) is size 3
/// assert!(solutions.iter().all(|s| s.iter().sum::<usize>() == 3));
/// ```
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct MaximumClique<G, W> {
    /// The underlying graph.
    graph: G,
    /// Weights for each vertex.
    weights: Vec<W>,
}

impl<G: Graph, W: Clone + Default> MaximumClique<G, W> {
    /// Create a MaximumClique problem from a graph with given weights.
    pub fn new(graph: G, weights: Vec<W>) -> Self {
        assert_eq!(
            weights.len(),
            graph.num_vertices(),
            "weights length must match graph num_vertices"
        );
        Self { graph, weights }
    }

    /// Get a reference to the underlying graph.
    pub fn graph(&self) -> &G {
        &self.graph
    }

    /// Get a reference to the weights.
    pub fn weights(&self) -> &[W] {
        &self.weights
    }

    /// Check if the problem uses a non-unit weight type.
    pub fn is_weighted(&self) -> bool
    where
        W: WeightElement,
    {
        !W::IS_UNIT
    }

    /// Check if a configuration is a valid clique.
    pub fn is_valid_solution(&self, config: &[usize]) -> bool {
        is_clique_config(&self.graph, config)
    }
}

impl<G: Graph, W: WeightElement> MaximumClique<G, W> {
    /// Get the number of vertices in the underlying graph.
    pub fn num_vertices(&self) -> usize {
        self.graph().num_vertices()
    }

    /// Get the number of edges in the underlying graph.
    pub fn num_edges(&self) -> usize {
        self.graph().num_edges()
    }
}

impl<G, W> Problem for MaximumClique<G, W>
where
    G: Graph + crate::variant::VariantParam,
    W: WeightElement + crate::variant::VariantParam,
{
    const NAME: &'static str = "MaximumClique";
    type Metric = SolutionSize<W::Sum>;

    fn variant() -> Vec<(&'static str, &'static str)> {
        crate::variant_params![G, W]
    }

    fn dims(&self) -> Vec<usize> {
        vec![2; self.graph.num_vertices()]
    }

    fn evaluate(&self, config: &[usize]) -> SolutionSize<W::Sum> {
        if !is_clique_config(&self.graph, config) {
            return SolutionSize::Invalid;
        }
        let mut total = W::Sum::zero();
        for (i, &selected) in config.iter().enumerate() {
            if selected == 1 {
                total += self.weights[i].to_sum();
            }
        }
        SolutionSize::Valid(total)
    }
}

impl<G, W> OptimizationProblem for MaximumClique<G, W>
where
    G: Graph + crate::variant::VariantParam,
    W: WeightElement + crate::variant::VariantParam,
{
    type Value = W::Sum;

    fn direction(&self) -> Direction {
        Direction::Maximize
    }
}

/// Check if a configuration forms a valid clique.
fn is_clique_config<G: Graph>(graph: &G, config: &[usize]) -> bool {
    // Collect all selected vertices
    let selected: Vec<usize> = config
        .iter()
        .enumerate()
        .filter(|(_, &v)| v == 1)
        .map(|(i, _)| i)
        .collect();

    // Check all pairs of selected vertices are adjacent
    for i in 0..selected.len() {
        for j in (i + 1)..selected.len() {
            if !graph.has_edge(selected[i], selected[j]) {
                return false;
            }
        }
    }
    true
}

crate::declare_variants! {
    MaximumClique<SimpleGraph, i32> => "1.1996^num_vertices",
}

/// Check if a set of vertices forms a clique.
///
/// # Arguments
/// * `graph` - The graph
/// * `selected` - Boolean slice indicating which vertices are selected
///
/// # Panics
/// Panics if `selected.len() != graph.num_vertices()`.
#[cfg(test)]
pub(crate) fn is_clique<G: Graph>(graph: &G, selected: &[bool]) -> bool {
    assert_eq!(
        selected.len(),
        graph.num_vertices(),
        "selected length must match num_vertices"
    );

    // Collect selected vertices
    let selected_vertices: Vec<usize> = selected
        .iter()
        .enumerate()
        .filter(|(_, &s)| s)
        .map(|(i, _)| i)
        .collect();

    // Check all pairs of selected vertices are adjacent
    for i in 0..selected_vertices.len() {
        for j in (i + 1)..selected_vertices.len() {
            if !graph.has_edge(selected_vertices[i], selected_vertices[j]) {
                return false;
            }
        }
    }
    true
}

#[cfg(test)]
#[path = "../../unit_tests/models/graph/maximum_clique.rs"]
mod tests;