Struct MinimumCostMaximumFlow 

pub struct MinimumCostMaximumFlow { /* private fields */ }

Minimum-Cost Maximum-Flow problem.

Variables

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

Example

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

// Diamond network from the canonical example.
let graph = DirectedGraph::new(4, vec![
    (0, 1), (0, 2), (1, 2), (1, 3), (2, 3),
]);
let problem = MinimumCostMaximumFlow::new(
    graph,
    0, 3,
    vec![2, 1, 1, 1, 2], // capacities
    vec![1, 0, 0, 1, 2], // costs
);
let solver = BruteForce::new();
let witness = solver.solve(&problem).unwrap().unwrap();
// Optimal flow has value 3 and cost 7.
assert_eq!(problem.flow_value(&witness).unwrap(), 3);
assert_eq!(problem.total_cost(&witness).unwrap(), 7);

Implementations

impl MinimumCostMaximumFlow

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

Create a new Minimum-Cost Maximum-Flow problem.

Panics

Panics if any of the following holds:

• capacities.len() != graph.num_arcs()
• costs.len() != graph.num_arcs()
• source >= graph.num_vertices()
• sink >= graph.num_vertices()
• source == sink
• Any capacity is negative
• Any cost is negative

pub fn graph(&self) -> &DirectedGraph

Get a reference to the underlying directed graph.

pub fn source(&self) -> usize

Get the source vertex.

pub fn sink(&self) -> usize

Get the sink vertex.

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

Get a reference to the arc capacities.

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

Get a reference to the arc costs.

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]) -> Result<bool, EvaluationError>

Check whether a flow assignment is feasible.

A flow is feasible iff

1. config.len() == num_arcs,
2. each 0 <= f(a) <= c(a), and
3. flow is conserved at every non-terminal vertex.

pub fn flow_value(&self, config: &[usize]) -> Result<i64, EvaluationError>

Compute the flow value |f| = net outflow from the source for a feasible configuration. Result is meaningless if config is not feasible.

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

Compute the total cost sum_a cost(a) * f(a) of a flow.

Trait Implementations

impl BruteForceProblem for MinimumCostMaximumFlow

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

Cardinality of each coordinate in the brute-force search space.

fn num_variables(&self) -> usize

Number of coordinates in the brute-force search space.

impl Clone for MinimumCostMaximumFlow

fn clone(&self) -> MinimumCostMaximumFlow

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MinimumCostMaximumFlow

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

Formats the value using the given formatter.

impl DeclaredVariant for MinimumCostMaximumFlow

impl<'de> Deserialize<'de> for MinimumCostMaximumFlow

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for MinimumCostMaximumFlow

const NAME: &'static str = "MinimumCostMaximumFlow"

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

type Solution = Vec<usize>

Mathematical witness type for this problem.

type Value = Min<i64>

The evaluation value type.

fn parameter_names() -> &'static [&'static str]

Canonical parameter names for this problem model.

fn parameters(&self) -> ProblemParameters

Measure the complete canonical parameters of this concrete instance.

fn evaluate(&self, config: &Self::Solution) -> Result<Min<i64>, EvaluationError>

Evaluate the problem on a solution.

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

Returns variant attributes derived from type parameters.

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) -> Result<Self::Result, ReductionError>

Reduce this problem to the target problem type.

fn target_construction(error: ConstructionError) -> ReductionError

where Self: Sized,

Attach this reduction edge to a target-construction failure.

fn exact_i64( value: usize, operation: impl Into<String>, ) -> Result<i64, ReductionError>

where Self: Sized,

Convert a structural count used by the target’s exact integer algebra.

impl Serialize for MinimumCostMaximumFlow

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.