In the R.I.N.G.S. code numerous analysis can be performed nevertheless CPU time is mainly driven by the ring statistics analysis, in particular by the maximum search depth, ie. the maximum size for a ring which is an input parameter fixed during the analysis .
This has been illustrated in figure [Fig. 1] which represents the evolution of the CPU time as a function of the maximum search depth.
As shown in figure [Fig. 1] the CPU times increase exponentially with the maximum search depth.
Furthermore we can see in figure [Fig. 1] that the evolution of the CPU time is similar in the cases of King, shortest path and primitive rings criteria (the CPU times for the strong ring criterion, not shown here, are much more important). Therefore the MPI parallelization appears fully justified to performed the ring statistics analysis of network material with a high search depth.