Module assignment 

Linear Assignment Problem solvers

The assignment problem finds the optimal one-to-one matching between agents and tasks that minimizes total cost.

Problem Definition

Given:

• n agents and m tasks (typically n = m)
• Cost matrix C where C[i][j] is cost of assigning agent i to task j

Find:

• Assignment minimizing sum of costs
• Each agent assigned to exactly one task
• Each task assigned to at most one agent

Algorithms

• hungarian - O(n⁴) Hungarian algorithm, simple and correct
• auction - O(n³) Auction algorithm, faster for sparse problems

Example

use converge_optimization::assignment::{solve, AssignmentProblem};

let problem = AssignmentProblem::from_costs(vec![
    vec![10, 5, 13],
    vec![3, 9, 18],
    vec![14, 8, 7],
]);

let solution = solve(&problem).unwrap();
println!("Total cost: {}", solution.total_cost);
for (agent, task) in solution.assignments.iter().enumerate() {
    println!("Agent {} -> Task {}", agent, task);
}

Modules

auction

Auction Algorithm for the Linear Assignment Problem

hungarian

Hungarian Algorithm for the Linear Assignment Problem

Structs

AssignmentProblem

An assignment problem instance

AssignmentSolution

Solution to an assignment problem

Traits

AssignmentSolver

Trait for assignment solvers

Functions

solve

Solve an assignment problem using the default solver (Hungarian)

solve_with_params

Solve an assignment problem with custom parameters