cutoff (to stop)

The algorithm will stop and conclude that the input sequence is not simplicial, if \(\tau_{\text{c}} \geq \text{cutoff}\). So this algorithm has false negatives, i.e., concluding that some input is not simplicial when it’s actually simplicial.

By default, \(\text{cutoff} = 10^5\).


On average, it takes longer to verify if a input is non-simplicial. You may wish to make cutoff larger, just to inspect thoroughly. But be warned that, the entire search tree grows combinatorially, as you might spend a long time, just to learn that the input is not simplicial.

How to set cutoff?

You should set a cutoff, to roughly 1e5 or larger (or you may wait forever for larger inputs).

There is only a small fraction of simplicial input sequence that will take a long time to determine, whereas there are a lot of hard non-simplicial inputs. Setting a moderate cutoff will avoid false negatives.