Resolving the intractability of the 'warehouseman's problem' using temporary storage space and other constraints

The coordination problem of rearranging rectangular blocks enclosed in a rectangular room, or the warehouseman's problem, which is known to be PSPACE-hard, is treated. The approach used is to find constraints that, when imposed on the general instance of a provably hard problem, lead to guaranteed polynomial-time solutions. The notion of reserving a portion of the available space for holding the blocks temporarily during the rearrangement process is introduced. This use of temporary storage space (TSS) helps to formalize the intuitive idea of available space, and puts restrictions on the actual distribution of free space. The TSS idea provides a way of parameterizing the control of the environment (using the area of the TSS) to observe its effect on the solution of the motion coordination problem. The other constraints are then used to lower the area of the TSS, since it is an overhead. The algorithms are given for square blocks in a square configuration, but can be easily modified to solve the more general problem with rectangular blocks in a rectangular configuration.<>