I would like to know if a program, using only linear programming, solves the problem; where for a size of n=20 it takes between 30 seconds and 10 minutes to solve it depending on the case. Would that program be efficient enough to be able to define its O(n) as a polynomial function?
I note that for several cases of n<20 tested they take the same, more or less time.

I cannot easily determine O(n) because for the same input size, the execution time varies depending on each case (the distances). I hope to be able to calculate O(n) by measuring the execution times and taking an average for each size.