Scheduling of parallel processing for regionally-constrained object placement selects between different balancing schemes. For a small number of movebounds, computations are assigned by balancing the placeable objects. For a small number of objects per movebound, computations are assigned by balancing the movebounds. If there are large numbers of movebounds and objects per movebound, both objects and movebounds are balanced amongst the processors. For object balancing, movebounds are assigned to a processor until an amortized number of objects for the processor exceeds a first limit above an ideal number, or the next movebound would raise the amortized number of objects above a second, greater limit. For object and movebound balancing, movebounds are sorted into descending order, then assigned in the descending order to host processors in successive rounds while reversing the processor order after each round. The invention provides a schedule in polynomial-time while retaining high quality of results.