Of Minimal Perimeter

The square decomposition problem has applications in a number of areas such as bin packing of flexible objects of fixed area and circuit layout with minimum communication requirements. Our interest in the square decomposition problem arises from the following problem in parallel computation [1]. One wishes to compute a table of all values of a binary function f on the Cartesian product S x T, where IS I = ] T I = m. The computation is to be performed in parallel on p processing units. The function values are computed as follows. The i-th processor computes the values of f on some subset W/of S x T. The sets W/, 1 _< i<_p, partition S x T. To minimize computation time, each processor is assigned an approximately equal number of function values to compute. Each processor has a small amount of local memory used for storing its operands. The objective is to minimize this storage. The