Levenshtein distance on Java-Dynamic programming

In information theory and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits.-Wikipedia
In practice, this distance can be used as the insertion key in a BK-tree used for auto-complete or spell checking, ie it is used in my JComplete project.

The dynamic programming approach in Java:

private int levenshtein(String string1, String string2) {

    int maxi = string1.length() + 1;

    int maxj = string2.length() + 1;

    int[][] distance = new int[maxi][maxj];



    for (int i = 1; i < maxi; i++) {

        distance[i][0] = i;

    }



    for (int j = 1; j < maxj; j++) {

        distance[0][j] = j;

    }



    for (int j = 1; j < maxj; j++) {

        for (int i = 1; i < maxi; i++) {

            if (string1.charAt(i - 1) == string2.charAt(j - 1)) {

                distance[i][j] = distance[i - 1][j - 1];

            } else {

                distance[i][j] = min(distance[i - 1][j] + 1,

                    distance[i][j - 1] + 1,

                    distance[i - 1][j - 1] + 1

                    );

            }

        }

    }

    return distance[maxi - 1][maxj - 1];

}