Struct BicliqueCover 

pub struct BicliqueCover { /* private fields */ }

The Biclique Cover problem.

Given a bipartite graph with vertex sets L and R, find k bicliques that together cover all edges. Each vertex can be in any subset of the k bicliques.

Example

use problemreductions::models::graph::BicliqueCover;
use problemreductions::topology::BipartiteGraph;
use problemreductions::{Problem, Solver, BruteForce};

// Bipartite graph: L = {0, 1}, R = {0, 1}
// Edges: (0,0), (0,1), (1,0) in bipartite-local coordinates
let graph = BipartiteGraph::new(2, 2, vec![(0, 0), (0, 1), (1, 0)]);
let problem = BicliqueCover::new(graph, 2);

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

// Check coverage
for sol in &solutions {
    assert!(problem.is_valid_cover(sol));
}

Implementations

impl BicliqueCover

pub fn new(graph: BipartiteGraph, k: usize) -> Self

Create a new Biclique Cover problem.

Arguments

• graph - The bipartite graph
• k - Number of bicliques

pub fn from_matrix(matrix: &[Vec<u8>], k: usize) -> Self

Create from a bipartite adjacency matrix.

Matrix[i][j] = 1 means edge between left vertex i and right vertex j.

pub fn graph(&self) -> &BipartiteGraph

Get the bipartite graph.

pub fn left_size(&self) -> usize

Get the left partition size.

pub fn right_size(&self) -> usize

Get the right partition size.

pub fn num_vertices(&self) -> usize

Get the number of vertices.

pub fn num_edges(&self) -> usize

Get the number of edges.

pub fn k(&self) -> usize

Get k (number of bicliques).

pub fn rank(&self) -> usize

Get the rank (alias for k()).

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

Check if a configuration is a valid biclique cover.

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

Check if the configuration is a valid biclique cover.

Under the classical definition, a biclique is a complete bipartite subgraph of the input graph: every pair (l, r) with l ∈ L_b and r ∈ R_b must be an edge of G. A configuration is a valid biclique cover iff every biclique is a sub-biclique of G and every edge of G is covered by at least one biclique.

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

Count covered edges.

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

Count total biclique size (sum of vertices in all bicliques).

Trait Implementations

impl Clone for BicliqueCover

fn clone(&self) -> BicliqueCover

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for BicliqueCover

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for BicliqueCover

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for BicliqueCover

const NAME: &'static str = "BicliqueCover"

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 Serialize for BicliqueCover

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 BicliqueCover