Struct ThreeDimensionalMatching 

pub struct ThreeDimensionalMatching { /* private fields */ }

Three-Dimensional Matching (3DM) problem.

Given disjoint sets W = {0, …, q-1}, X = {0, …, q-1}, Y = {0, …, q-1} and a set M of triples (w, x, y) where w is in W, x is in X, y is in Y, determine if there exists a subset M’ of M with |M’| = q such that no two triples in M’ agree in any coordinate.

This is a classical NP-complete problem (Karp, 1972), closely related to Exact Cover by 3-Sets.

Example

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

// W = X = Y = {0, 1, 2} (q = 3)
// Triples: (0,1,2), (1,0,1), (2,2,0), (0,0,0), (1,2,2)
let problem = ThreeDimensionalMatching::new(
    3,
    vec![(0, 1, 2), (1, 0, 1), (2, 2, 0), (0, 0, 0), (1, 2, 2)],
);

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

// First three triples form a valid matching
assert!(!solutions.is_empty());
assert!(problem.evaluate(&solutions[0]));

Implementations

impl ThreeDimensionalMatching

pub fn new(universe_size: usize, triples: Vec<(usize, usize, usize)>) -> Self

Create a new 3DM problem.

Panics

Panics if any triple contains an element outside 0..universe_size.

pub fn universe_size(&self) -> usize

Get the universe size (q).

pub fn num_triples(&self) -> usize

Get the number of triples in M.

pub fn triples(&self) -> &[(usize, usize, usize)]

Get the triples.

pub fn get_triple(&self, index: usize) -> Option<&(usize, usize, usize)>

Get a specific triple.

Trait Implementations

impl Clone for ThreeDimensionalMatching

fn clone(&self) -> ThreeDimensionalMatching

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ThreeDimensionalMatching

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for ThreeDimensionalMatching

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for ThreeDimensionalMatching

const NAME: &'static str = "ThreeDimensionalMatching"

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 ReduceTo<ILP> for ThreeDimensionalMatching

type Result = ReductionThreeDimensionalMatchingToILP

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl ReduceTo<ThreePartition> for ThreeDimensionalMatching

type Result = ReductionThreeDimensionalMatchingToThreePartition

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl Serialize for ThreeDimensionalMatching

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 ThreeDimensionalMatching