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 ⁿ. The authors present a recurrence equation model defining the target problems for systolic program derivation. Some geometrical tools on convex polyhedra in Zⁿ 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