Let's say I have an algorithm that can be tuned by a parameter $h>0$ and is expected to converge as $h\to 0$.
I want to study the computational complexity of this algorithm, i.e., how the required runtime increases with increasing accuracy. For this purpose, I run the algorithm for different values of $h$ (say, $h_1>h_2>\dots>h_n>\dots >h_N$) and summarize the accuracy (computed in comparison to a different, established method, with high accuracy) and runtime of these runs in a plot.
The plot shows runtime on the horizontal axis and accuracy on the vertical axis. However, sometimes, the runtimes are non-monotonic as I increase $n$. Should I reorder the runs so as to have a plot where the accuracy is a function of the work?
For example, the plots may look like this if I just connect run $n$ to run $n+1$:
Note that run $n=2$ took more time than run $n=3$ but also ended up being more accurate.
The reordered plot would look as below. Note that the data points have not changed, they are just connected in a different order.