Struct BMF 

pub struct BMF { /* private fields */ }

The Boolean Matrix Factorization problem.

Given an m x n boolean matrix A and rank k, find:

• B: m x k boolean matrix
• C: k x n boolean matrix

Such that B * C = A exactly, minimizing the total number of 1s in B and C. Configurations that do not yield an exact factorization are infeasible.

Example

use problemreductions::models::algebraic::BMF;
use problemreductions::{Problem, Solver, BruteForce};

// 2x2 identity matrix — boolean rank 2
let a = vec![
    vec![true, false],
    vec![false, true],
];
let problem = BMF::new(a, 2);

let solver = BruteForce::new();
let witness = solver.find_witness(&problem).unwrap();
assert!(problem.is_exact(&witness));

Implementations

impl BMF

pub fn new(matrix: Vec<Vec<bool>>, k: usize) -> Self

Create a new BMF problem.

Arguments

• matrix - The target m x n boolean matrix
• k - The factorization rank

pub fn rows(&self) -> usize

Get the number of rows.

pub fn cols(&self) -> usize

Get the number of columns.

pub fn rank(&self) -> usize

Get the factorization rank.

pub fn m(&self) -> usize

Get the number of rows (alias for rows()).

pub fn n(&self) -> usize

Get the number of columns (alias for cols()).

pub fn matrix(&self) -> &[Vec<bool>]

Get the target matrix.

pub fn extract_factors( &self, config: &[usize], ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>)

Extract matrices B and C from a configuration.

Config layout: first mk bits are B (row-major), next kn bits are C (row-major).

pub fn boolean_product(b: &[Vec<bool>], c: &[Vec<bool>]) -> Vec<Vec<bool>>

Compute the boolean product B * C.

(B * C)[i,j] = OR_k (B[i,k] AND C[k,j])

pub fn hamming_distance(&self, config: &[usize]) -> usize

Compute the Hamming distance between the target and the product.

pub fn is_exact(&self, config: &[usize]) -> bool

Check if the factorization is exact (Hamming distance = 0).

pub fn total_factor_size(&self, config: &[usize]) -> usize

Total number of 1s in B and C (the factor size to be minimized when exact).

Trait Implementations

impl Clone for BMF

fn clone(&self) -> BMF

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for BMF

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for BMF

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for BMF

const NAME: &'static str = "BMF"

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

type Value = Min<i32>

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]) -> Min<i32>

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<BMF> for BicliqueCover

type Result = ReductionBicliqueCoverToBMF

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<BicliqueCover> for BMF

type Result = ReductionBMFToBicliqueCover

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<ILP> for BMF

type Result = ReductionBMFToILP

The reduction result type.

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

Reduce this problem to the target problem type.

impl Serialize for BMF

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 BMF