Optimized collision check for all pairs using bounding volume hierarchy

Question

I am working on broad-phase collision detection. I understood how to build a bounding volume hierarchy using AABB's as bounding volumes. I also understood how to check all collisions of a single AABB against all other AABB's

My concern now is to check for all pairs. I don't want to do a single body against all bodies check, which will result roughly in a O(n*logn) complexity. I think we can do much better once we build up the hierarchy but I can't figure out how.

Edit: I have come up with a solution and made it open-source: https://bitbucket.org/ttrkaya/broad-phase-bounding-volume-hierarchy

Answer 1

I have come up with a solution myself and made it open-source: https://bitbucket.org/ttrkaya/broad-phase-bounding-volume-hierarchy