## 5 Experimental Results
### Inference Rate Maximization

Table 6: Normalized results for DN\({}^{2}\)PCIoT 30R and DN\({}^{2}\)PCIoT after approaches. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Setup**} & **Median** & **Per** & **Per** & **Greedy** & **iRgreedy** & **iRgreedy** & **METIS** & **METIS** \\  & **of 30** & **Layers** & **Layers** & **2:1** & **1:1** & **2:1** & **1:1** & **2:1** & **1:1** \\  & **Random** & **2:1** & **2:1** & **2:1** & **1:59** & **1:61** & **1:36** & **1:13** & **1:23** \\ \hline
2 free & 6.35 & 1.67 & 1.67 & 1.59 & 1.59 & 1.61 & 1.36 & 1.13 & 1.23 \\
4 free & 4.09 & x & x & 2.06 & 2.06  
could produce valid partitionings. The quality of these results was due to the heavy unbalanced partitioning in the per-layer approach, which overloaded one device while a low load was assigned to the other device, as the least constrained setup offered two devices. The state-of-the-art tool METIS also led to suboptimal results because it attempts to balance all the constraints, which are memory and computational load. Additionally, several partitionings provided by METIS were invalid because METIS does not consider a limit for the amount of memory in each partition. METIS could not produce any valid partitionings at all for the 56- and 63-device experiments because METIS cannot properly account for the memory required by the shared parameters and biases of CNNs. One way to solve this issue would be to add the memory required by the shared parameters and biases to every vertex that needs them, even if the vertices were assigned to the same partition. However, this solution would require much more memory and no partitioning using this solution would be valid for the setups used in this work. Thereby, we gave METIS the LeNet model without the memory information required by the shared parameters and biases in the hope that it would produce valid partitionings since our setups provided enough memory for LeNet and one full set of shared parameters and biases for each device. Unfortunately, METIS was not able to produce any valid partitionings in any of the 56- and 63-device constrained setups. Finally, the greedy algorithm and the _iRgreedy_ approach are simple approaches. Although they produced poor results, they could produce valid partitionings for all the proposed setups. Thus, considering the ability to produce valid partitionings, these approaches demonstrated to be better than METIS and the per-layer partitioning offered by popular ML frameworks in the proposed setups. In Table 6, we can see that DN\({}^{2}\)PCIoT starting from the partitioning produced by the other approaches also achieved results that range from intermediate to the best results. When comparing to the state-of-the-art tool METIS, DN\({}^{2}\)PCIoT after METIS could improve the METIS result by up to 38%. Additionally, DN\({}^{2}\)PCIoT after approaches is a better approach when compared to DN\({}^{2}\)PCIoT 30R because DN\({}^{2}\)PCIoT after approaches do not need to run 30 times to attempt to find the best partitioning as in the DN\({}^{2}\)PCIoT 30R. Furthermore, the single execution required by DN\({}^{2}\)PCIoT after each approach may run faster than DN\({}^{2}\)PCIoT 30R because it starts from the intermediate result achieved by the other approaches instead of a random partitioning that usually requires several epochs to stop. DN\({}^{2}\)PCIoT after the greedy algorithm result also show the robustness of DN\({}^{2}\)PCIoT because the greedy algorithm produced the worst results mostly. Nevertheless, DN\({}^{2}\)PCIoT after greedy could improve the poor results of the greedy algorithm up to 11.1 times, yielding at least intermediate results in comparison to the other approaches. The LeNet 1:1 model runs in a considerably larger time than the LeNet 2:1 model due to the difference in the number of vertices and edges of the graphs. When comparing the two LeNet models used in the experiments, it is possible to see that DN\({}^{2}\)PCIoT for LeNet 2:1 led to the best result in 80% of the experiments.