Detecting string similarity using Levenshtein distance (is SLOW)

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myTable row count is 150000 rows. I need to compare the values in NAME column. If I detect similarity <= similarity level and if the NUM column values are the same I should log it.
They way I loop through this table takes forever. What other solutions are there?

DataTable dt1 = new DataTable();
dt1.Load(DbInfo.DataRdr(Conn, "SELECT * FROM myTable"));
for (int i = 0; i < dt1.Rows.Count; i++)
{
 for (int j = 0; i + 1 < dt1.Rows.Count; j++)
 {
   if (dt1.Rows[i]["NUM"].ToString() == dt1.Rows[j]["NUM"].ToString())
   {
      if (dt1.Rows[i]["Name"].ToString().
LevenshteinDistance(dt1.Rows[j]["Name"].ToString()) <= 10)
      {
        Logging.Write(...);
       }
   }
  }
}
    public static int LevenshteinDistance(this string s, string t)
    {
        if (s == null)
            throw new ArgumentNullException("s");
        if (t == null)
            throw new ArgumentNullException("t");
        int n = s.Length;
        int m = t.Length;
        int[,] d = new int[n+1,m+1];
        if (n == 0 || m == 0)
            return Math.Max(m, n);
        for (int i = 0; i <= n; i++)
        {
            d[i, 0] = i;
        }
        for (int i = 0; i < m; i++)
        {
            d[0, i] = i;
        }
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                int cost = (t[j] == s[i]) ? 0 : 1;
                d[i + 1, j + 1] = Math.Min(Math.Min(d[i, j + 1] + 1, d[i + 1, j] + 1), d[i, j] + cost);
            }
        }
        return d[n, m];
    }myTable row count is 150000 rows.
I need to compare the values in NAME column. If I detect similarity <= similarity level and if the NUM column values are the same I should log it. 

They way I loop through this table takes forever. What other solutions are there?

<pre lang="cs">DataTable dt1 = new DataTable();
dt1.Load(DbInfo.DataRdr(Conn, "SELECT * FROM myTable"));

   for (int i = 0; i < dt1.Rows.Count; i++)
   {

     for (int j = 0; j < dt1.Rows.Count; j++)
     {
       if (dt1.Rows[i]["Name"].ToString().LevenshteinDistance(dt1.Rows[j]            ["Name"].ToString()) <= 10)
       {
          if (dt1.Rows[i]["NUM"].ToString() == dt1.Rows[i]["NUM"].ToString())
          {
            Logging.Write(...);
           }
       }
      }

  }

Posted 8-Jul-11 9:27am

Mastersev

Updated 8-Jul-11 9:54am

v2

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2 solutions

Solution 1

You can start with

for (int j = i + 1; j < dt1.Rows.Count; j++)

since once two words have been compared, the inverse is always the same number.

Posted 8-Jul-11 9:37am

dbrenth

Comments

Mastersev 8-Jul-11 15:39pm

thx

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Philippe Mori · Accepted Answer · 2011-07-08T15:10:00

Assuming that you are only interested in similar words, then you can modify LevenshteinDistance so that you will stop comparing 2 strings as soon as the maximum similarity level has been reached.

public static int? LevenshteinDistance(this string s, string t, 
    int similarityLimit)
{
    // Some code...

    // In the inner loop, add:
    if (cost > similarityLevel)
    {
        return null;
    }
}

And in calling code:

int limit = 10;
int? similarity = LevenshteinDistance(row1, row2, limit);
bool isSimilar = similarity.HasValue && similarity.Value <= limit;

Assuming that a lot of pairs have a cost much higher than the limit, it will greatly reduce the execution time.

Then since you are only interested to know if NAME ar similar when NUM are equal, then you might be able to reverse those 2 tests since the second one (a string comparison) should be much faster. Thus you can eliminate most calls to LevenshteinDistance assuming that NUM are not all equals.

Thus your inner loop might look like this:

SQL

// First do the "fast" check
if (dt1.Rows[i]["NUM"].ToString() == dt1.Rows[i]["NUM"].ToString())
{
    // Then do the "slow" check...
    if (dt1.Rows[i]["Name"].ToString().LevenshteinDistance(
        dt1.Rows[j]["Name"].ToString()) <= 10)
    {
        Logging.Write(...);
    }
}

Then assuming that you have more than a few percents of NUM that are equals, you can sort items by their NUM. One way to do it would be to sort the data returned by the reader using a query like:

SELECT * FROM myTable ORDER BY NUM

If the database is indexed, it might be the faster option. Otherwise, it might be done by using something like Dictionary<string, List<int>> where each distinct NUM are added to the dictionary and the list is filled with the indexes in the table.

C#

var numDictionary = new Dictionary<string, List<int>>;
for (int i = 0; i < dt1.Rows.Count; i++)
{
    var rowNum = dt1.Rows[i]["NUM"].ToString();

    List<int> listIndexes;
    if (!numDictionary.TryGetValue(rowNum, out listIndexes))
    {
        list = new List<int>;
        numDictionary.Add(rowNum, list);
    }
    list.Add(i);
}

Then you can compute the LevenshteinDistance for each list in the dictionary using nested loop as you have done in the original algorithm.

Note that the internal loop can stop at the index of the external loop. That is, stop just before j is equal to i.

If the order does not matters, then you can write items in the log directly. If not, fill some structures with the information you wil need to output and sort that structure before outputting the results.