it strictly non-blocking, are $m=3$ and $p=6$, which means there exists more than $5\times$ as much overhead compared to a blocking CSTN with the same $n$, resulting in a significant increase in the area and delay overhead. To avoid such large overhead, we employ a *close to non-blocking CSTN* described in [@shyy1991log] to implement the CSTN-RCSTN pair. This network is able to generate not all, but *almost all* permutations, while it could be implemented using a $LOG_{n, log_2(n) - 2, 1}$ configuration, meaning it needs $log_2(n) - 2$ extra stages and no additional copy. Fig. \[CSTN\_arch\](b), demonstrates an example of such a near non-blocking CSTN with $n = 8$.

Based on the structure of CSTN/RCSTN, and the size used for implementation, the size of configuration bits ($S$) would be changed. For instance, for a near non-blocking $LOG_{64, 4, 1}$, the number of selectors is 960 $(2log_2(64) - 2)(32)(3)$ (3 selectors in each $2 \times 2$ switches (Fig. \[CSTN\_arch\])). Based on the size of configuration, and the number of messages that could be sent in each interval ($T$), the overhead (time/energy) would be changed in *ExTru*. However, we show that since ($T$) is large enough, the performance boost, as well as 