VA-DE: Valuable ATAPE with dynamic embedding and super-pipeline scheduling on partitionable multistage interconnection networks+

Abstract

The optimal ATAPE (all-to-all personalized exchange) is a key solution to achieve the optimal communication in parallel matrix-transposition, parallel fast-Fourier-transformation, etc. The ATAPE has been extensively studied on static networks and dynamic binary-switch MINs (multistage interconnection networks). Recently, the ultimate ATAPE was successfully embedded on MINs+ and the fast crossbar of MINs+. However, the MINs+ cannot be partitioned for multiple tasks and the crossbar of MINs+ is more expensive and less subsystem-utilization. Therefore, this paper proposes the prototype of the x×x crossbar of partitionable MINs+ (PMINs+) using I/O cross-control switches and the generalized d-nary-switch MINs+. In addition, the optimal VA-DE (valuable ATAPE with dynamic embedding) with triple-right scheduling (right-task, right-section, right-time) is presented for multiple tasks of flexible sizes N″=N/2t (where t≤log2x) and the efficient subsystem-utilization on the PMINs+. New partitionable ATAPE embedding and automatic mapping for the partitionable section y(=0 to x−1) are Dy=Sy⊕Cly (global) and lDy=(Dy%N″)⊕cz (local) using double-jumping controls Cly=(yN/x+l)modN (to right section) and cz=zN″/x (to right subtask), incorporated with super-pipelining for outperforming optimal time O(N/x) over O(N), the best of existing ATAPEs. In experiments, remarkable speedup and throughput were strongly confirmed on the simulated PMIN+ systems.