THEORY AND ALGORITHMS FOR FACE HYPERCUBE EMBEDDING

We present a new matrix formulation of the face hypercube embedding pr oblem that motivates the design of an efficient search strategy to fin d an encoding that satisfies all faces of minimum length. Increasing d imensions of the Boolean space are explored; for a given dimension con straints are satisfied one at a time. The following features help to r educe the nodes of the solution space that must be explored: candidate cubes instead of candidate codes are generated, cubes yielding symmet ric solutions are not generated, a smaller sufficient set of solutions (producing basic sections) is explored, necessary conditions help dis card unsuitable candidate cubes, early detection that a partial soluti on cannot be extended to be a global solution prunes infeasible portio ns of the search tree. We have implemented a prototype package minimum input satisfaction kernel (MINSK) based on the previous ideas and run experiments to evaluate it. The experiments show that MINSK is faster and solves more problems than any available algorithm. Moreover, MINS K is a robust algorithm, while most of the proposed alternatives are n ot. Besides most problems of the complete Microelectronics Center of N orth Carolina (MCNC) benchmark suite, other solved examples include an important set of decoder programmable logic arrays (PLA's) coming fro m the design of microprocessor instruction sets.