Fat-trees: Universal networks for hardware-efficient supercomputing

The author presents a new class of universal routing networks, called fat-trees, which might be used to interconnect the processors of a general-purpose parallel supercomputer. A fat-tree routing network is parameterized not only in the number of processors, but also in the amount of simultaneous communication it can support. Since communication can be scaled independently from the number of processors, substantial hardware can be saved for such applications as finite-element analysis without resorting to a special-purpose architecture. It is proved that a fat-tree of a given size is nearly the best routing network of that size. This universality theorem is established using a three-dimensional VLSI model that incorporates wiring as a direct cost. In this model, hardware size is measured as physical volume. It is proved that for any given amount of communications hardware, a fat-tree built from that amount of hardware can stimulate every other network built from the same amount of hardware, using only slightly more time (a polylogarithmic factor greater).