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

Abstract

In single chip multiprocessors (CMP) with grid topologies, a significant part of power consumption is attributed to communications between the cores of the grid. We investigate the problem of routing communications between CMP cores using shortest paths, in a model in which the power cost associated with activating a communication link at a transmission speed of f bytes/second is proportional 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 grids depends on the ability to split communication requests between a given pair of node, routing each such request along multiple paths. For a pair of cores in a m × n grid, the number of available communication paths between them grows exponentially with n, m. By contrast, we show that optimal power consumption (up to constant factors) can be achieved by splitting each communication request into k paths, starting from a threshold value of k = Θ(n 1/(α−1) ). This threshold is much smaller than n for typical values of α ≈ 3, and may be considered practically feasible for use in routing schemes on the grid. More generally, we provide efficient algorithms for routing multiple k-splittable communication requests between two cores in the grid, providing solutions within a constant approximation of the optimum cost. We support our results with algorithm simulations, showing that for practical instances, our approach using k-splittable requests leads to a power cost close to that of the optimal solution with arbitrarily splittable requests, starting from the stated threshold value of k.