Constraint Satisfaction Problem Solver

This is a TypeScript library for expressing and solving constraint satisfaction problems, originally developed by Niels Joubert. It solves discrete finite-domain problems via recursive backtracking.

Example

Install the package via:

npm install constraint-satisfaction-problem

It can then be used like so:

// ES Module
import { CSP } from "constraint-satisfaction-problem";

// CommonJS
// const { CSP } = require("constraint-satisfaction-problem");

const csp = new CSP();

csp.addVariable("a", [1,2,3]);
csp.addVariable("b", [4,5,6]);
csp.addVariable("c", [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]);

csp.addConstraint(
	["a", "b"],
	function(a, b) { return a*2 === b; }
);

csp.addConstraint(
	["b", "c"],
	function(b, c) { return b*2 === c; }
);

// { a: 2, b: 4, c: 8 }
const oneSolution = csp.getSingleSolution();
console.log(oneSolution);

// [ { a: 2, b: 4, c: 8 }, { a: 3, b: 6, c: 12 } ]
const allSolutions = csp.getAllSolutions();
console.log(allSolutions);

Intro to CSPs

What is a CSP?

A Constraint Satisfaction Problem is formally defined as:

• A set of variables, Xi ... Xn
• Each variable has a domain of values it can take, Di ... Dn
• A set of constraints Ci ... Cn that specifies allowable combinations of values for a subset of the variables.

That is, a set of variables, with relations between the valid values of these variables.

There are multiple classes of CSPs:

• Discrete problems, where the values of each variable can be enumerated
• Finite problems, where the size of domain is finite
• Continuous problems, where the values of each variable is a range
• Infinite problems, where the domain of a variable is of infinite extent

Then there are subclasses of these:

• Integer problems, discrete infinite problems on the integers
• Binary constraint problems, where all the constraints are between two variables
• Linear problems, where all the constraints are linear
• Integer Linear problems, where all the constraints are linear and the values integers. This is the hardest kind of constraint problem.
• And many more...

Examples of real-world CSPs

There are tons and tons of problems that can reduce to constraint satisfaction problems, and it is a rich field of study. But, here's some that everyone knows about:

• Sudoku
• Coloring maps
• Scheduling blocks of time

Credits

This project started as a port of the python-constraint library.

This library was originally developed by Niels Joubert. I have taken his code and modernized it to current JavaScript ecosystem standards, for publishing on NPM.