Splittable Single Source-Sink Routing on CMP Grids: A Sublinear Number of Paths Suffice

In single chip multiprocessors (CMP) with grid topologies, a significant part of power consump-tion is attributed to communications between the cores of the grid. We investigate the problem ofrouting communications between CMP cores using shortest paths, in a model in which the powercost associated with activating a communication link at a transmission speed of f bytes/second isproportional to f α , for some constant exponent α > 2.Our main result is a trade-off showing how the power required for communication in CMP gridsdepends on the ability to split communication requests between a given pair of node, routing eachsuch request along multiple paths. For a pair of cores in a m×n grid, the number of available com-munication paths between them grows exponentially with n,m. By contrast, we show that optimalpower consumption (up to constant factors) can be achieved by splitting each communication requestinto k paths, starting from a threshold value of k = Θ(n1/(α−1)). This threshold is much smaller thann for typical values of α ≈ 3, and may be considered practically feasible for use in routing schemeson the grid. More generally, we provide efficient algorithms for routing multiple k-splittable commu-nication requests between two cores in the grid, providing solutions within a constant approximationof the optimum cost. We support our results with algorithm simulations, showing that for practicalinstances, our approach using k-splittable requests leads to a power cost close to that of the optimalsolution with arbitrarily splittable requests, starting from the stated threshold value of k.