For derivative calculations, debugging, and interactive control one may need to reverse the execution of a computer program for given inputs. If any increase of the time needed for the reversal is unacceptable, the availability of enough auxiliary processors provides the possibility to reverse the computer program with minimal temporal complexity and a surprisingly small spatial complexity using parallel reversal schedules. This paper describes the structure of such parallel reversal schedules that use the checkpointing technique on a multi-processor machine. They are shown to require the least number of processors and memory locations to store checkpoints given a certain number of time steps.