Struct DirectedTwoCommodityIntegralFlow 

pub struct DirectedTwoCommodityIntegralFlow { /* private fields */ }

Directed Two-Commodity Integral Flow problem.

Given a directed graph G = (V, A) with arc capacities c(a), two source-sink pairs (s_1, t_1) and (s_2, t_2), and requirements R_1, R_2, determine whether two integral flow functions f_1, f_2: A -> Z_0^+ exist such that:

1. Joint capacity: f_1(a) + f_2(a) <= c(a) for all a in A
2. Flow conservation: for each commodity i, flow is conserved at every vertex except its own source and sink
3. Requirements: net flow into t_i under f_i is at least R_i

Variables

2|A| variables: first |A| for commodity 1’s flow on each arc, next |A| for commodity 2’s flow on each arc. Variable j for arc a of commodity i ranges over {0, …, c(a)}.

Example

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

// 6-vertex network: s1=0, s2=1, t1=4, t2=5
let graph = DirectedGraph::new(6, vec![
    (0, 2), (0, 3), (1, 2), (1, 3),
    (2, 4), (2, 5), (3, 4), (3, 5),
]);
let problem = DirectedTwoCommodityIntegralFlow::new(
    graph, vec![1; 8], 0, 4, 1, 5, 1, 1,
);
let solver = BruteForce::new();
assert!(solver.find_witness(&problem).is_some());

Implementations

impl DirectedTwoCommodityIntegralFlow

pub fn new( graph: DirectedGraph, capacities: Vec<u64>, source_1: usize, sink_1: usize, source_2: usize, sink_2: usize, requirement_1: u64, requirement_2: u64, ) -> Self

Create a new Directed Two-Commodity Integral Flow problem.

Panics

Panics if:

• capacities.len() != graph.num_arcs()
• Any terminal vertex index >= graph.num_vertices()

pub fn graph(&self) -> &DirectedGraph

Get a reference to the underlying directed graph.

pub fn capacities(&self) -> &[u64]

Get a reference to the capacities.

pub fn source_1(&self) -> usize

Get source vertex for commodity 1.

pub fn sink_1(&self) -> usize

Get sink vertex for commodity 1.

pub fn source_2(&self) -> usize

Get source vertex for commodity 2.

pub fn sink_2(&self) -> usize

Get sink vertex for commodity 2.

pub fn requirement_1(&self) -> u64

Get requirement for commodity 1.

pub fn requirement_2(&self) -> u64

Get requirement for commodity 2.

pub fn num_vertices(&self) -> usize

Get the number of vertices.

pub fn num_arcs(&self) -> usize

Get the number of arcs.

pub fn max_capacity(&self) -> u64

Get the maximum capacity across all arcs.

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

Check whether a flow assignment is feasible.

config has 2*|A| entries: first |A| for commodity 1, next |A| for commodity 2.

Trait Implementations

impl Clone for DirectedTwoCommodityIntegralFlow

fn clone(&self) -> DirectedTwoCommodityIntegralFlow

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DirectedTwoCommodityIntegralFlow

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for DirectedTwoCommodityIntegralFlow

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for DirectedTwoCommodityIntegralFlow

const NAME: &'static str = "DirectedTwoCommodityIntegralFlow"

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

type Value = Or

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]) -> Or

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<DirectedTwoCommodityIntegralFlow> for KSatisfiability<K3>

type Result = Reduction3SATToDirectedTwoCommodityIntegralFlow

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<ILP<i32>> for DirectedTwoCommodityIntegralFlow

type Result = ReductionD2CIFToILP

The reduction result type.

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

Reduce this problem to the target problem type.

impl Serialize for DirectedTwoCommodityIntegralFlow

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 DirectedTwoCommodityIntegralFlow