Struct MinimumCostCirculation 

pub struct MinimumCostCirculation { /* private fields */ }

Minimum-Cost Circulation problem.

Variables

|A| variables: variable a ranges over {0, ..., c(a)} representing the integral circulation on arc a.

Example

use problemreductions::models::graph::MinimumCostCirculation;
use problemreductions::topology::DirectedGraph;
use problemreductions::{Problem, Solver, BruteForce};

// Two competing cycles 0->1->0 and 0->2->0; the cheaper-per-unit
// cycle 0->2->0 has lower capacity, but pushing both to capacity is
// optimal.
let graph = DirectedGraph::new(3, vec![
    (0, 1), (1, 0), (0, 2), (2, 0),
]);
let problem = MinimumCostCirculation::new(
    graph,
    vec![2, 2, 1, 1],   // capacities
    vec![2, -3, 1, -4], // costs (signed)
);
let solver = BruteForce::new();
let witness = solver.find_witness(&problem).unwrap();
// Optimal cost = 2*2 + 2*(-3) + 1*1 + 1*(-4) = -5.
assert_eq!(problem.total_cost(&witness), -5);

Implementations

impl MinimumCostCirculation

pub fn new(graph: DirectedGraph, capacities: Vec<i64>, costs: Vec<i64>) -> Self

Create a new Minimum-Cost Circulation problem.

Panics

Panics if any of the following holds:

• capacities.len() != graph.num_arcs()
• costs.len() != graph.num_arcs()
• Any capacity is negative

Note: costs are signed and may be negative.

pub fn graph(&self) -> &DirectedGraph

Get a reference to the underlying directed graph.

pub fn capacities(&self) -> &[i64]

Get a reference to the arc capacities.

pub fn costs(&self) -> &[i64]

Get a reference to the arc costs (signed).

pub fn num_vertices(&self) -> usize

Get the number of vertices |V|.

pub fn num_arcs(&self) -> usize

Get the number of arcs |A|.

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

Check whether a circulation assignment is feasible.

A circulation is feasible iff

1. config.len() == num_arcs,
2. each 0 <= g(a) <= c(a), and
3. inflow equals outflow at every vertex (no exempt terminals — this is what distinguishes a circulation from a flow).

pub fn total_cost(&self, config: &[usize]) -> i64

Compute the total cost sum_a a(a) * g(a) of a circulation.

Trait Implementations

impl Clone for MinimumCostCirculation

fn clone(&self) -> MinimumCostCirculation

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MinimumCostCirculation

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for MinimumCostCirculation

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for MinimumCostCirculation

const NAME: &'static str = "MinimumCostCirculation"

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

type Value = Min<i64>

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<i64>

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<MinimumCostCirculation> for MinimumCostMaximumFlow

type Result = ReductionMCMFToMCC

The reduction result type.

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

Reduce this problem to the target problem type.

impl Serialize for MinimumCostCirculation

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 MinimumCostCirculation