Optimal Self-Routing Split Modules for Radix-based Interconnection Networks

Radix-based interconnection networks recursively partition the messages according to the most significant bits of their target addresses. The required split modules are usually implemented by binary sorting networks or by permutation networks. While sorting networks are self-routing, it can be proven that permutation networks cannot be self-routing so that they require additional configuration logic which is not required for sorting networks. In this paper, we point out that sorting networks are however not the best self-routing split modules. In particular, we first use our previous work to construct better self-routing split modules from sorting networks. Second, we show that even if the best sorting networks are used for the latter construction, we can still find better self-routing split modules. To determine optimal self-routing split modules, we reduce the problem to an equivalent model-checking problem. Using this, we derive provably optimal-depth and optimal-size self-routing split modules for small numbers of inputs.