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A recent work proposed to simplify fat-trees with adaptive routing by means of a load-balancing deterministic routing algorithm. The resultant network has performance figures comparable to the more complex adaptive routing fat-trees when packets need to be delivered in order. In a second work by the same authors published in IEEE CAL, they propose to simplify the fat-tree to a unidirectional multistage interconnection network (UMIN), using the same load-balancing deterministic routing algorithm. They show that comparable performance figures are achieved with much lower network complexity. In this comment we show that the proposed load-balancing deterministic routing is in fact the routing scheme used by the butterfly network. Moreover we show that the properties of the simplified UMIN network proposed by them are intrinsic to the standard butterfly and other existing UMINs.