Exact Strong Radius and Diameter of 3-Dimensional Grid Networks

—Building efficient strongly connected directed paths in three-dimensional (3D) grid networks is foundational for minimizing communication latencies and ensuring deterministic data routing in large-scale interconnected systems. This paper explores how to orient these networks to achieve the shortest possible distances across the entire structure. We first establish tight theoretical lower bounds for two key metrics: the minimum achievable worst-case strong distance from an optimal center to all nodes (orientable strong radius) and the minimum achievable worst-case strong distance between any pair of nodes (orientable strong diameter). To reach these limits, we propose two structured methods. The first algorithm, termed Convergent-Divergent Orientation, coordinates coordinate-driven flows to enhance reachability from the network center. The second algorithm, the Layer-Flip Checkerboard Orientation, removes unnecessary detours to shrink the overall network travel distance to its absolute physical limit. By replacing unpredictable random paths with our structured design, we eliminate performance spikes and hidden efficiency losses. This provides a reliable and scalable solution for high-performance 3D interconnected systems.