X-Y-Z Optimization: Minimal Routing for 3-D Mesh Networks

The introduction of 3-D silicon integration technology has shifted the entire concentration to extend the 2-D mesh based tiled chip multiprocessor architectures into three dimensions. There have been various routing algorithms proposed and implemented to route the data in 2-D mesh networks. But their performance degrades tremendously when extended to 3-D mesh networks. A new routing algorithm, RPM (randomized partially-minimized) was proposed to achieve efficient routing in 3-D mesh networks. RPM achieves optimal worst-case throughput for 3-D mesh networks when the network radix k is even and within a factor of 1/k of optimal worst-case throughput when k is odd. Although RPM achieves optimal worst case throughput, the average latency achieved is not optimal because it routes packets non-minimally in one of the three dimensions. This paper focuses on developing an efficient routing algorithm, XYZO (X-Y-Z Optimization) for 3-D mesh networks to achieve minimal routing in all the three dimensions and hence the optimal average latency. A search router is employed in addition to the existing architecture to find the shortest path between the source and destination in the network and leverage the load balancing properties of the network traffic through minimal routing in all three dimensions. The paper also endorses parallelism and concurrency in computation. Keywords— Algorithm/protocol design and analysis; Interprocessor communications; Network Architecture and Design; Routing protocols.