Question

Is there a fast algorithm for finding the Largest Common Substring in two strings or is it an NPComplete problem?

In PHP I can find a needle in a haystack:

<?php  if (strstr('there is a needle in a haystack', 'needle')) {     echo 'found<br>\n'; } ?> 

I guess I could do this in a loop over one of the strings but that would be very expensive! Especially since my application of this is to search a database of email and look for spam (i.e. similar emails sent by the same person).

Does anyone have any PHP code they can throw out there?

Answer 1

I have since found a relevant wikipedia article. It is not a NP complete problem, it can be done in O(mn) time using a dynamic programming algorithm.

In PHP I found the similar_text function very useful. Here’s a code sample to retrieve a series of text emails and loop through them and find ones that are 90% similar to each other. Note: Something like this is NOT scalable:

<?php // Gather all messages by a user into two identical associative arrays $getMsgsRes = mysql_query(SELECT * FROM email_messages WHERE from = '$someUserID'); while($msgInfo = mysql_fetch_assoc($getMsgsRes)) {     $msgsInfo1[] = $msgInfo;     $msgsInfo2[] = $msgInfo; }  // Loop over msgs and compare each one to every other foreach ($msgsInfo1 as $msg1)     foreach ($msgsInfo2 as $msg2)         similar_text($msg1['msgTxt'],$msg2['msgTxt'],$similarity_pst);         if ($similarity_pst > 90)             echo "{$msg1['msgID']} is ${similarity_pst}% to {$msg2['msgID']}\n"; ?>