Any thoughts on how to automatically avoid rest collisions in polyphonic music?

[David Bellows]

So sorry everyone, I forgot to use reply all. Here's my latest message:

Ok, this all might be confusing so I've attached two example pngs
showing the collisions. The use_rest.png file uses rests like c'4/rest
while no_rest just uses regular rests like r4. I know I could
manipulate these manually to avoid the rests but getting things to
work automatically is the trick.

no_rest.png
Description: PNG image

use_rest.png
Description: PNG image