How to reduce swellig after knee replacement surgery?

Lots of things. Ice it a lot. Get a knee sleeve ice machine and use it when ever you are sitting down or resting for the first 6-12 weeks. I can't stress how much these ice machine sleeves help. Bregg makes a great machine. I believe it is called polar tec. Do lots of isometric quadriceps contractions. Elevate it when your not walking around. Ice after any activity for 10-20 minutes. Where a compression sock.
Compression. Ice, elevation, compression, and +/- nsaids (under the advice of your surgeon) can all help. Sometimes, the knee will be warm and swollen for 6+ months after the surgery.