I first read about this idea in the AMLE Magainze . Select a few key problems from the previous night's assignment and use them as a quiz or bell-ringer at the start of class.
If students feel they need to do the homework to pass the quiz, they'll do the homework. If a student can pass the quiz without doing the homework, did they really need to do the assignment? You're still getting useful data about what your students know and don't know AND holding students accountable for their learning without taking class time (or home time) to grade full daily assignments.