Unblocking Placement and Routing in Rearrangeable Multi-Stage Networks

High-performance computing demands efficient and scalable interconnections. Although crossbar networks offer high parallel bandwidth, their $O\left(n^2\right)$ costs are prohibitively expensive. Multi-stage networks provide scalability with $O\left(n\log n\right)$ cost, yet they may block certain routing patterns. Rearrangeable multistage networks (RMNs) have emerged as a cost-effective solution, enabling internal connection rearrangements to make all paths accessible without network blocking. However, discovering optimal rearrangement strategies remains a challenge for unblocking large-scale (256 connections) reconfigurable networks. We advance the state of the art by effectively managing workloads with over 50% without blocking. When nearly all connections are required, we introduce routing strategies to rearrange existing connections. In the presence of multicast, where the configuration space exceeds $10^{671}$, we propose novel strategies employing simulated annealing for placement and Monte Carlo tree search for routing to prioritize multicast connections, which simultaneously maximize the number of connections by minimizing conflicts and reducing the number of extra stages. To the best of our knowledge, we first demonstrate that the Benes network is not rearrangeable under multicast conditions. We propose exploring the rearrangeability of shuffle exchanges with additional network stages.