Struct SchedulingToMinimizeWeightedCompletionTime 

pub struct SchedulingToMinimizeWeightedCompletionTime { /* private fields */ }

Scheduling to Minimize Weighted Completion Time problem.

Given a set T of tasks with processing times l(t) and weights w(t), and a number m of identical processors, find an assignment of tasks to processors that minimizes the total weighted completion time sum_t w(t) * C(t), where C(t) = start_time(t) + l(t).

Within each processor, tasks are ordered by Smith’s rule: non-decreasing l(t)/w(t) ratio. The only free variables are the processor assignments.

Representation

Each task has a variable in {0, ..., m-1} representing its processor assignment, giving dims() = [m; n].

Example

use problemreductions::models::misc::SchedulingToMinimizeWeightedCompletionTime;
use problemreductions::{Problem, BruteForce};
use problemreductions::types::Min;

// 5 tasks, 2 processors
let problem = SchedulingToMinimizeWeightedCompletionTime::new(
    vec![1, 2, 3, 4, 5], vec![6, 4, 3, 2, 1], 2,
);
let solver = BruteForce::new();
let witness = solver.solve(&problem).unwrap().unwrap();
assert_eq!(problem.evaluate(&witness).unwrap(), Min(Some(47)));

Implementations

impl SchedulingToMinimizeWeightedCompletionTime

pub fn new(lengths: Vec<i64>, weights: Vec<i64>, num_processors: usize) -> Self

Create a new scheduling instance.

Panics

Panics if lengths.len() != weights.len(), if num_processors is zero, or if any length or weight is zero.

pub fn max_processing_time_bits(&self) -> u64

Smallest h >= 1 bounding every processing time in magnitude strictly by 2^h.

pub fn num_tasks(&self) -> usize

Returns the number of tasks.

pub fn num_processors(&self) -> usize

Returns the number of processors.

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

Returns the processing times.

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

Returns the task weights.

Trait Implementations

impl BruteForceProblem for SchedulingToMinimizeWeightedCompletionTime

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 SchedulingToMinimizeWeightedCompletionTime

fn clone(&self) -> SchedulingToMinimizeWeightedCompletionTime

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SchedulingToMinimizeWeightedCompletionTime

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

Formats the value using the given formatter.

impl DeclaredVariant for SchedulingToMinimizeWeightedCompletionTime

impl<'de> Deserialize<'de> for SchedulingToMinimizeWeightedCompletionTime

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for SchedulingToMinimizeWeightedCompletionTime

const NAME: &'static str = "SchedulingToMinimizeWeightedCompletionTime"

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

Returns variant attributes derived from type parameters.

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

Evaluate the problem on a solution.

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl ReduceTo<ILP<i64, i64, Bounded>> for SchedulingToMinimizeWeightedCompletionTime

type Result = ReductionSMWCTToILP

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 SchedulingToMinimizeWeightedCompletionTime

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

where __S: Serializer,

Serialize this value into the given Serde serializer.