Struct ThreeMatroidIntersection 

pub struct ThreeMatroidIntersection { /* private fields */ }

Three-Matroid Intersection problem.

Given three partition matroids on a common ground set E = {0, …, n-1} and a positive integer K ≤ |E|, determine whether there exists a subset E’ ⊆ E such that |E’| = K and E’ is independent in all three matroids.

A partition matroid is defined by a partition of E into groups. A set S is independent if |S ∩ G| ≤ 1 for every group G.

While 2-matroid intersection is solvable in polynomial time (Edmonds, 1970), the jump to three matroids captures NP-hardness.

Example

use problemreductions::models::set::ThreeMatroidIntersection;
use problemreductions::{Problem, Solver, BruteForce};

// Ground set E = {0, 1, 2, 3, 4, 5}, K = 2
let problem = ThreeMatroidIntersection::new(
    6,
    vec![
        vec![vec![0, 1, 2], vec![3, 4, 5]],       // M1
        vec![vec![0, 3], vec![1, 4], vec![2, 5]],  // M2
        vec![vec![0, 4], vec![1, 5], vec![2, 3]],  // M3
    ],
    2,
);

let solver = BruteForce::new();
let solutions = solver.find_all_witnesses(&problem);
assert!(!solutions.is_empty());

Implementations

impl ThreeMatroidIntersection

pub fn new( ground_set_size: usize, partitions: Vec<Vec<Vec<usize>>>, bound: usize, ) -> Self

Create a new Three-Matroid Intersection problem.

Panics

Panics if:

• partitions does not contain exactly 3 matroids
• Any element index is outside 0..ground_set_size
• bound exceeds ground_set_size

pub fn ground_set_size(&self) -> usize

Get the ground set size.

pub fn partitions(&self) -> &[Vec<Vec<usize>>]

Get the three partition matroids.

pub fn bound(&self) -> usize

Get the bound K.

pub fn num_groups(&self) -> usize

Get the total number of groups across all three matroids.

Trait Implementations

impl Clone for ThreeMatroidIntersection

fn clone(&self) -> ThreeMatroidIntersection

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ThreeMatroidIntersection

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for ThreeMatroidIntersection

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for ThreeMatroidIntersection

const NAME: &'static str = "ThreeMatroidIntersection"

Base name of this problem type (e.g., “MaximumIndependentSet”).

type Value = Or

The evaluation value type.

fn dims(&self) -> Vec<usize>

Configuration space dimensions. Each entry is the cardinality of that variable.

fn evaluate(&self, config: &[usize]) -> Or

Evaluate the problem on a configuration.

fn variant() -> Vec<(&'static str, &'static str)>

Returns variant attributes derived from type parameters.

fn num_variables(&self) -> usize

Number of variables (derived from dims).

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl Serialize for ThreeMatroidIntersection

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl DeclaredVariant for ThreeMatroidIntersection