podlomar / stable-marriages

Implementation of the extended Gale-Shapley algorithm for finding all stable marriages

stable-marriages

Implementation of the extended Gale-Shapley algorithm for recursively finding all solutions to The stable marriage problem

Installation

npm install stable-marriages

Usage

First, import the Instance and StablePairings classes.

import { Instance, StablePairings } from "stable-marriages";

An instance of size (for example) 8 has 8 man on one side and 8 women on the other side. Men and women have numbers from 0 to 7. For an instance of size 8 you need to provide two 8x8 matrices with all the preference lists, one matrix for men, one matrix for women. In each matrix an array on index i represents the preference list of man/woman with number i.

const instance = Instance.create(8, [
  [2, 0, 4, 6, 3, 1, 7, 5],
  [5, 0, 2, 3, 7, 6, 4, 1],
  [6, 3, 2, 5, 4, 0, 1, 7],
  [4, 2, 7, 1, 5, 0, 3, 6],
  [3, 0, 1, 7, 6, 2, 5, 4],
  [5, 1, 4, 6, 7, 3, 2, 0],
  [6, 7, 0, 5, 1, 2, 3, 4],
  [1, 5, 6, 0, 7, 2, 3, 4],
], [
  [3, 2, 7, 0, 1, 4, 6, 5],
  [2, 6, 4, 7, 5, 3, 0, 1],
  [6, 4, 7, 2, 5, 1, 0, 3],
  [5, 3, 1, 6, 2, 0, 4, 7],
  [7, 6, 0, 4, 5, 3, 2, 1],
  [4, 3, 6, 5, 1, 7, 2, 0],
  [0, 3, 4, 5, 1, 7, 2, 6],
  [1, 4, 3, 2, 6, 7, 0, 5],
]);

Getting all stable pairings:

const stablePairings = new StablePairings(instance);
const pairings = stablePairings.compute();

For this particulast instance you should get 23 pairings. Each pairing is represented by the Pairing class. You can get the paired men and women from, say, the first pairing by looking at the array pairings[0].pairs.

console.log(pairings[0].pairs)
// [2, 0, 6, 4, 3, 5, 7, 1]

This says that man 0 is paired with women 2, man 1 with women 0 etc.

Performance

The algorithm has worst case exponential complexity but for most random cases runs under few seconds for instances of size up to 800.

The implementation is very basic and there are optimizations that could be added in the future.