Before revision:  Finally we run computational experiments on random points, which show that Minibox filtrations can often be used to reduce the number of simplices included in \v{C speed up persistent homology computations  .
After revision:  Finally we run computational experiments on random points, which show that Minibox filtrations can often be used to reduce the number of simplices included in \v{C speed up persistent homology computations in homological degrees zero and one by reducing the number of simplices in the filtration .