Pairs vs. particle radius s for a homogeneous disk with a ≤ a_max = 2au, I ≤ 10⁻³, ϵ ≤ 10⁻³, and with N = 10⁴, from Aliberti (2022a,b). Orange: twice the number of pairs that needed to be checked in the apoapsis/periapsis filter. Blue: actual number of collision possibilities. The guideline with slope 1 (dashed) shows the approximate linear dependence of the collision pairs on s. The influence of the planet size can be seen in the apoapsis/periapsis filter for large s. Because there are two collision possibilities for each pair, the blue dots lie below or on the orange dots.