Are there advantages to high-dimension architectures?: Analysis of k-ary n-cubes for the class of parallel divide-and-conquer algorithms

Previous work analyzing k-my n-cubes with constant bisecrian-width und constant node-degree constraints have shown that generally lowerdtmenslon and middle-dimen.~ion cubes, respectively, have the best performance in terms of message [atencles under cantentimr, These analyses were done u.wummg a randam dtstrvbutian of ’me.wage traffic with same k)caliz,afion probabdiry, and da not necessarily capture the actual comrnunicatian patterns of many well-designed parallel application.v. In this work, we analyze.’ theoretically and empirically, the perjimmance of k -ary n-cubes ,for the class of diwde-and-conquer (D&C) parallel algorithms that are u.fedfor solvarg many numerical and non-numerical computations. We cla.wi~ D& C parallel algorithms accarding w their camrnunication patterns, and campare the perj%rrnance of three different classes qfthese alganthms on k-ary n-cubes In agreement with previous work, our results show that under the constant bmecrion-width constraint, the 2-D mesh perjarms best, the hypercube has the lowest perfarntance, and m general a lower dimension M better than a Iagher one, Howeve~ unhke prewarrs results ,for the more reahstm constant node-degree constraint (pin limitations on proce.worlrouter chips quickly become the overriding constraint as system size increases) that show that middle-dimenswna[ cubes have the lowest latencies, we show that the hypercube has the best perjorrnance, the 2-D mesh the warst, and generally that a }ugher dlmen. non IS better than a lower one,