Struct OptimumCommunicationSpanningTree 

pub struct OptimumCommunicationSpanningTree { /* private fields */ }

The Optimum Communication Spanning Tree problem.

Given a complete graph K_n with edge weights w(e) >= 0 and communication requirements r(u,v) >= 0 for each vertex pair, find a spanning tree T minimizing the total communication cost:

sum_{u < v} r(u,v) * W_T(u,v)

where W_T(u,v) is the weight of the unique path between u and v in T.

Representation

Each edge of K_n is assigned a binary variable (0 = not in tree, 1 = in tree). Edges are ordered lexicographically: (0,1), (0,2), …, (0,n-1), (1,2), …, (n-2,n-1). A valid spanning tree has exactly n-1 selected edges forming a connected subgraph.

Example

use problemreductions::models::misc::OptimumCommunicationSpanningTree;
use problemreductions::{Problem, Solver, BruteForce};

let problem = OptimumCommunicationSpanningTree::new(
    vec![
        vec![0, 1, 2],
        vec![1, 0, 3],
        vec![2, 3, 0],
    ],
    vec![
        vec![0, 1, 1],
        vec![1, 0, 1],
        vec![1, 1, 0],
    ],
);
let solver = BruteForce::new();
let solution = solver.find_witness(&problem);
assert!(solution.is_some());

Implementations

impl OptimumCommunicationSpanningTree

pub fn new(edge_weights: Vec<Vec<i32>>, requirements: Vec<Vec<i32>>) -> Self

Create a new OptimumCommunicationSpanningTree instance.

Arguments

• edge_weights - Symmetric n x n matrix with w(i,i) = 0 and w(i,j) >= 0.
• requirements - Symmetric n x n matrix with r(i,i) = 0 and r(i,j) >= 0.

Panics

Panics if the matrices are not square, not the same size, have nonzero diagonals, are not symmetric, or contain negative entries.

pub fn num_vertices(&self) -> usize

Returns the number of vertices.

pub fn num_edges(&self) -> usize

Returns the number of edges in the complete graph K_n.

pub fn edge_weights(&self) -> &Vec<Vec<i32>>

Returns the edge weight matrix.

pub fn requirements(&self) -> &Vec<Vec<i32>>

Returns the requirements matrix.

pub fn edges(&self) -> Vec<(usize, usize)>

Returns the list of edges in lexicographic order: (0,1), (0,2), …, (n-2,n-1).

pub fn edge_index(i: usize, j: usize, n: usize) -> usize

Map a pair (i, j) with i < j to its edge index.

Trait Implementations

impl Clone for OptimumCommunicationSpanningTree

fn clone(&self) -> OptimumCommunicationSpanningTree

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for OptimumCommunicationSpanningTree

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for OptimumCommunicationSpanningTree

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for OptimumCommunicationSpanningTree

const NAME: &'static str = "OptimumCommunicationSpanningTree"

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

type Value = Min<i64>

The evaluation value type.

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

Returns variant attributes derived from type parameters.

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

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

fn evaluate(&self, config: &[usize]) -> Min<i64>

Evaluate the problem on a configuration.

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 OptimumCommunicationSpanningTree

type Result = ReductionOptimumCommunicationSpanningTreeToILP

The reduction result type.

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

Reduce this problem to the target problem type.

impl Serialize for OptimumCommunicationSpanningTree

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 OptimumCommunicationSpanningTree