An implementation of the Levenshtein distance using two arrays instead of a matrix, as in: https://gist.github.com/andrei-m/982927

levenshtein.js

/*
 * The MIT License (MIT)
 *
 * Copyright (c) 2014 Jacopo Notarstefano
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.

 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

exports.levenshteinDistance = function (a, b) {
        var i, j, firstRow = [], secondRow = [];

        if (a.length === 0) return b.length;
        if (b.length === 0) return a.length;

        for (i = 0; i <= b.length; i++) {
                firstRow[i] = i;
        }

        for (i = 1; i <= a.length; i++) {
                secondRow[0] = i;
                for (j = 1; j <= b.length; j++) {
                        if (a.charAt(i - 1) === b.charAt(j - 1)) {
                                secondRow[j] = firstRow[j - 1];
                        } else {
                                secondRow[j] = 1 + Math.min(firstRow[j - 1],
                                                firstRow[j], secondRow[j - 1]);
                        }
                }

                for (j = 0; j <= b.length; j++) {
                        firstRow[j] = secondRow[j];
                }
        }

        return secondRow[b.length];
}