Switch Adjusting on Hierarchical Shuffle-Exchange Networks for All-to-All Personalized Exchange

The original all-to-all personalized exchange algorithms were introduced for static interconnection networks (i.e., hypercube, mesh, and torus). Later, the all-to-all personalized exchange methods were extended for dynamic interconnection networks or MINs (Multistage Interconnection Networks i.e., omega (or shuffle exchange), flip, cube, and baseline) with N = 2(n) (= 4, 8, 16, 32, ...). Recently, the generalized all-to-all personalized exchange algorithm was designed for shuffle-exchange networks with even N (= 4, 6, 8, 10,...). However, for a hierarchical shuffle-exchange network, those existing algorithms cannot be directly applied. This paper introduces such a hierarchical MIN along with switch-adjusting function, operated by shift logic in O(1), for applying all-to-all personalized exchange and other parallel point-to-point permutations successfully. Finally, correctness of our switch adjusting on hierarchical shuffle-exchange networks is verified for all-to-all personalized exchange permutations.