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This letter presents a new oblivious routing algorithm for 3D mesh networks called randomized partially-minimal (RPM) routing that provably achieves optimal worst- case throughput for 3D meshes when the network radix fc is even and within a factor of 1/k 2 of optimal when k is odd. Although this optimality result has been achieved with the minimal routing algorithm OITURN for the 2D case, the worst-case throughput of OITURN degrades tremendously in higher dimensions. Other existing routing algorithms suffer from either poor worst-case throughput (DOR, ROMM) or poor latency (VAL). RPM on the other hand achieves near optimal worst-case and good average-case throughput as well as good latency performance.
Pao et al. (Tue,) studied this question.