Run time as a function of the number of bins, expressed in arbitrary units. Data points in the top panel show the amount of time needed to reach a simulation time of t = 1 in units of initial collision times. Data points in the bottom panel show the time needed to run for 400 steps. Blue points and curves are for the ﹩{ \mathcal O }({N}^{2})﹩ algorithm, and red ones are for the ﹩{ \mathcal O }({N}^{3})﹩ algorithm. Solid lines are the best-fit power law to all the points, assuming the slopes to be exactly 2 and 3. Dotted lines are the best-fit power laws determined without fixing the slope. See text for more details.