Efficient off-line routing of permutations on restricted access expanded delta networks

Abstract

This paper presents an off-line algorithm for routing permutations on expanded delta networks (EDNs) with restricted access. Restricted access means that the number of elements to be permuted may exceed the number of inputs to the EDN. For every N-element permutation on an M-input EDN, the algorithm computes a routing that takes exactly 3N/M passes (assuming M divides N). On a certain class of EDNs, the number of passes can be reduced to 2N/M. For example, for every 16 K-element permutation on the 1 K-input global network of the MasPar MP-1 and MP-2, the algorithm computes a routing that takes exactly 32 passes. The time complexity of the algorithm is Theta (NlogN) sequentially, and Theta (log/sup 2/N) on an N-processor PRAM.<>