Decomposition of Total Exchange for Multidimensional Interconnects

ious data permutations occurring e.g. in parallel FFT ..and basic linear algebra algorithms can be viewed as Total exchange is an important collectIve communzinstances of the total exchange problem [2]. cation pro~lem in multip.roces~or i.ntercon~~tion netIn this work we present general theory for solving works. It znvolves the dzssemznatlon of dzstlnct mesthe total exchange problem in multidimensional netsages from every node t.o every other no~e. We pres~~t works. A multitude of quantities or properties in such a novel theory for solvzng the problem zn any multldznetworks can be decomposed to quantities and propermensional ( cartesian product! netw?rk. .We con.s~ruct ties of the individual dimensions. We show here that a general algorithm and provzde optlmahty ~n~ztlons. the total exchange problem can also be decomposed It is seen that many of the popular topologzes, .zncl~dto the simpler problem of performing total exchange ing hyperc~~es, k-ary n-cubes and general ton satIsfy in single dimensions. This is a major simplification to these condztlons. The results we present here apply to an inherently complex problem. We provide a general the single-port model. algorithm applicable to any multidimensional network given that we have total exchange algori~hms for ~ac.h dimension. Optimality conditions are given and It IS