Before asking the question, I should say that I am not sure here is a proper community to ask this question or not.
I have an NP-hard problem and an optimization to deal with the problem. Recently, I have found that the problem has a phase transition where, before a threshold for a property, the problem can be solved in polynomial time by a greedy approach and, difficult cases are after the threshold.
Now, I want to show this phase transition by some parameters related to the optimization that solves the problem. But, I don't know which parameters can show this phase transition in a valid way, like time-solving, the number of iterations to solve the problem, or .....