Munkres

A lightweight and efficient implementation of the Munkres (Hungarian) algorithm for optimal assignment.

Features

1. Flexible

   • Use number or bigint matrices.
   • Use square (NxN) or rectangular (MxN) matrices.
   • Works with any MatrixLike input. Use arrays, typed arrays, custom objects, etc.

2. Fast (benchmarks)

   • O(M2N) when M <= N

   • O(MN2) when M > N

3. Efficient

   • O(M + N) memory

4. Robust

   • Supports -Infinity and Infinity values.
   • Helper methods provided for creating and modifying matrices.

Getting Started

Install

NPM:

npm install munkres

Yarn:

yarn add munkres

JSR:

jsr add @munkres/munkres

Usage

With a cost matrix:

import munkres from "munkres";

// Create a cost matrix. Cell [y, x] is the cost
// of assigning the y-th worker to the x-th job.
const costMatrix = [
  [1, 2, 3],
  [2, 4, 6],
  [3, 6, 9],
];

// Find a set of optimal assignments pairs (y, x).
const assignments = munkres(costMatrix);

console.log(assignments);
// Output: [[0, 2], [1, 1], [2, 0]]

With a profit matrix:

import { munkres, copyMatrix, invertMatrix } from "munkres";

// Create a profit matrix. Cell [y, x] is the
// profit of assigning the y-th worker to the x-th job.
const profitMatrix = [
  [9, 8, 7],
  [8, 6, 4],
  [7, 4, 1],
];

// Covert the profit matrix into a cost matrix.
const costMatrix = copyMatrix(profitMatrix);
invertMatrix(costMatrix);

// Find a set of optimal assignments pairs (y, x).
const assignments = munkres(costMatrix);

console.log(assignments);
// Output: [[0, 2], [1, 1], [2, 0]]

API

• munkres(costMatrix)

  Executes the Munkres algorithm on the given cost matrix and returns a set of optimal assignment pairs. Even if there are multiple optimal assignment sets, only one is returned.

Types

• Matrix<T>: A generic 2D matrix (i.e. T[][]).

• MatrixLike<T>: A generic read-only 2D matrix.

  • Can be made from any ArrayLike objects (i.e. any indexable object with a numeric length property). This allows for more flexibility, such as matrices made with typed arrays or objects.

• Pair<A, B = A>: A generic pair (i.e. [A, B]).

Helpers

1. copyMatrix(matrix): Creates a copy of the given matrix.

2. createMatrix(workers, jobs, callbackFn): Generates a matrix based on the given workers, jobs, and callback function.

3. genMatrix(numRows, numCols, callbackFn): Generates a matrix based on the given dimensions and a callback function.

4. getMatrixMax(matrix): Finds the maximum value in a given matrix.

5. getMatrixMin(matrix): Finds the minimum value in a given matrix.

6. invertMatrix(matrix, bigVal?): Inverts the values in the given matrix. Useful for converting between minimizing and maximizing problems. If bigVal is not given, the matrix's max value is used instead.

7. negateMatrix(matrix): Negates all values in the given matrix. Useful for converting between minimizing and maximizing problems.

Community and Support

Contributions are welcome!

• Questions / Dicussions: Please contact us via GitHub discussions.

• Bug Reports: Please use the GitHub issue tracker to report any bugs. Include a detailed description and any relevant code snippets or logs.

• Feature Requests: Please submit feature requests as issues, clearly describing the feature and its potential benefits.

• Pull Requests: Please ensure your code adheres to the existing style of the project and include any necessary tests and documentation.

For more information, check out the contributor's guide.

Build

1. Clone the project from github

git clone [email protected]:havelessbemore/munkres.git
cd munkres

2. Install dependencies

npm install

3. Build the project

npm run build

This will output ECMAScript (.mjs) and CommonJS (.js) modules in the dist/ directory.

Format

To run the code linter:

npm run lint

To automatically fix linting issues, run:

npm run format

Test

To run tests:

npm test

To run tests with a coverage report:

npm run test:coverage

A coverage report is generated at ./coverage/index.html.

Benchmarks

Run benchmarks in your browser.

To run locally:

npm run bench

CI / CD

Benchmarks are integrated into our CI/CD pipeline and automatically run with each commit to the main branch. This helps monitor the performance impacts of development, preventing regressions and verifying changes maintain performance standards.

View historical results.

Specs:

• Package version: latest
• Runtime: NodeJS v20
• Benchmarking Tool: tinybench v2.6.0
• OS: ubuntu-latest

Results

Below are the latest results from running locally.

Specs:

• Package version: v2.0.2
• Runtime: NodeJS v20.12.2
• Benchmarking Tool: tinybench v2.6.0
• Machine:
  • Model: MacBook Air
  • Chip: Apple M2
  • Memory: 8 GB
  • OS: MacOS Sonoma

number[][]

| Dimensions | Min (ms) | Max (ms) | Avg (ms) | Samples | | ---------- | ----------- | ----------- | ----------- | --------- | | 2x2 | 0 | 0.92475 | 0.00014 | 3,611,437 | | 4x4 | 0.00013 | 0.38683 | 0.00041 | 1,227,622 | | 8x8 | 0.00062 | 0.2005 | 0.00134 | 372,763 | | 16x16 | 0.002 | 0.26346 | 0.00487 | 102,720 | | 32x32 | 0.009 | 0.06462 | 0.01874 | 26,678 | | 64x64 | 0.04483 | 0.28279 | 0.07837 | 6,381 | | 128x128 | 0.228 | 0.52058 | 0.34338 | 1,457 | | 256x256 | 1.07725 | 2.37567 | 1.59139 | 315 | | 512x512 | 5.86442 | 9.18546 | 7.71347 | 65 | | 1024x1024 | 31.82083 | 45.471 | 38.12961 | 50 | | 2048x2048 | 165.45792 | 245.93154 | 205.5154 | 50 | | 4096x4096 | 905.25592 | 1,384.78808 | 1,129.78629 | 50 | | 8192x8192 | 5,062.63533 | 7,561.39129 | 6,152.11964 | 50 |

bigint[][]

| Dimensions | Min (ms) | Max (ms) | Avg (ms) | Samples | | ---------- | ------------ | ------------ | ------------ | --------- | | 2x2 | 0.00004 | 1.45567 | 0.00018 | 2,763,520 | | 4x4 | 0.00029 | 0.61792 | 0.00058 | 860,516 | | 8x8 | 0.00121 | 0.63829 | 0.00246 | 203,435 | | 16x16 | 0.0045 | 0.639 | 0.00994 | 50,320 | | 32x32 | 0.02021 | 0.66221 | 0.04299 | 11,633 | | 64x64 | 0.11575 | 1.00283 | 0.19514 | 2,563 | | 128x128 | 0.53988 | 1.92654 | 0.9169 | 546 | | 256x256 | 3.32492 | 6.38088 | 4.51322 | 112 | | 512x512 | 15.75375 | 46.94746 | 25.27091 | 50 | | 1024x1024 | 107.30771 | 171.37271 | 129.81464 | 50 | | 2048x2048 | 546.04767 | 850.22892 | 689.95893 | 50 | | 4096x4096 | 2,835.29229 | 4,583.96688 | 3,697.85205 | 50 | | 8192x8192 | 18,069.79829 | 24,171.88267 | 21,107.47192 | 10 |

Made with ❤️ by Michael Rojas