Calculus of space-optimal mappings of systolic algorithms on processor arrays

The authors present a method for the mapping of systolic algorithms that use the minimal number of processors. This method is based on geometrical interpretations on convex polyhedra in Z/sup n/. The authors present a recurrence equation model defining the target problems for systolic program derivation. Some geometrical tools on convex polyhedra in Z/sup n/ are given. They are first used to model systolic timing allocation in terms of geometrical structures, and then to deduce a processor array mapping method that automatically gives space-optimal mappings. The results are used to derive two space-optimal mappings of the Gaussian elimination algorithm.< >