The Trash Compactor Debate turns on whether the Death Star ejects its trash into space. I, for one, believe it does. Though we never see the Death Star ejecting its trash, we do see another Empire ship, the so-called Star Destroyer, ejecting its trash into space. I therefore see no reason to suspect that Empire protocol dictating that trash be ejected into space would not apply equally to all Empire spacecraft, including the Death Star.
The read be here.