How would implement StackExchange ‘Questions with similar titles’ for the FAQ on my wordpress site

I want to have a FAQ page on my site which has a search box. As the user types in their question, a field below the search box is populated with FAQ answers with similar titles.

The exact same functionality as the StackExchange ‘Questions with similar titles’ feature:

Questions with similar titles

4 Open Source Forum for wordpress
similar to stackexchange or
stackoverflow (1)

0 How to implement a WordPress
comments function? (2)

etc…

The communication with the server happens via Ajax. I once wrote a high-level overview of Ajax in WordPress, but you can find many more examples on this site and around the web.

Next, you have to do a query that will find similar titles. I found some questions that might help you on Stack Overflow:

• Suggestion For Finding Similar Rows In Mysql
• Display similar results from mySQL
• Is Full Text search the answer?