Optimal data reduction on reconfigurable tori

Data reduction is a fundamental operation of parallel computing. We derive lower bounds on communication latency for global data reduction and multiple global data reduction on reconfigurable tori. We present optimal global data reduction algorithms and multiple global data reduction algorithms on reconfigurable tori of any dimension. The formal reduction algorithms we give can make reduction and broadcast operations in [5][6][7] easy to implement.link_to_subscribed_fulltex