Mapping algorithms for permutation networks*

The mapping problem arises when the dependency structure of a parallel algorithm differs from the interconnection of processors in the intended parallel computer (topological variation) or, when the number of processes required by the algorithm exceeds the number of processors available in the computer (cardinality variation). The problem discussed in this paper is to identify a distributed computing environment that best optimizes the objective function for the given problem. Distinct network permutations may result in equivalent process permutation depending upon t,he mapping of processes onto the processors. In this paper we study the permuting properties of d y n m ic interconnection networks taking process mapping into consideration. A uniform group theoretic representation for interconnection networks is developed. Finally, an algorithm to evaluate the number of passes required by an interconnection network t,o realize a given mapping is presented.