Fastest Index/Algorithm to find similar sentences

Hi,

I'm searching for an algorithm/Index to find similar sentences in a database.

The Fulltextsearch is not really suitable because it doesn't have a tolerance.

The Levenshtein-distance ist to slow.

I also tried pg_trgm module, which works with tri-grams, but it's also very slow with 100.000+ rows.

I hope someone can help, I can't really find sth. which is fast enough.

Best regards,
Janek