Theoretical algorithmic efficiency: number of computational steps (big O) for one orbital period vs. particle count N. Blue: intersecting Kepler orbits without secular dynamics. Orange: with secular dynamics. The blue dotted line indicates where precession due to secular dynamics cannot be neglected. The black line shows the estimated number of steps for a tree code and/or spatial hashing. The slopes of the lines are 3, 2, and 4/3, respectively.