Near-Optimal Oblivious Routing on Three-Dimensional Mesh Networks

The increasing viability of three dimensional (3D) silicon integration technology has opened new opportunities for chip architecture innovations. One direction is in the extension of two-dimensional (2D) mesh-based tiled chip-multiprocessor architectures into three dimensions. In this paper, we focus on efficient routing algorithms for such 3D mesh networks. As in the case of 2D mesh networks, throughput and latency are important design metrics for routing algorithms. Existing routing algorithms suffer from either poor worst-case throughput (DOR [1], ROMM [3]) or poor latency (VAL [2]). Although the minimal routing algorithm O1TURN proposed in [4] already achieves near-optimal worst-case throughput for the 2D case, the optimality result does not extend to higher dimensions. For 3D and higher dimensional meshes, the worst-case throughput of O1TURN degrades tremendously. The main contribution of this paper is the design of a new oblivious routing algorithm for 3D mesh networks called Randomized Partially-Minimal (RPM) routing. RPM provably achieves optimal worst-case throughput for 3D meshes when the network radix k is even and within a factor of l/k(2) of optimal worst-case throughput when k is odd. RPM also outperforms VAL, DOR, ROMM, and O1TURN in average-case throughput by 33.3%, 111%, 47%, and 30%, respectively when averaged over one million random traffic patterns on an 8 x 8 x 8 topology. Finally, whereas VAL achieves optimal worst-case throughput at a penalty factor of 2 in average latency over DOR, RPM achieves (near) optimal worst-case throughput with a much smaller factor of 1.33. In practice, the average latency of RPM is expected to be closer to minimal routing because 3D mesh networks are not expected to be symmetric in 3D chip designs. The number of available device layers is expected to be much less than the number of processor tiles that can be placed along an edge of a device layer, For practical asymmetric 3D mesh configurations, the average latency of RPM reduces to just a factor of 1.11 of DOR.