The scenario A chain of points: (P_i)_i=0,N where P_i is linked to its direct neighbours (P_i-1 and P_i+1).

The goal: perform efficient collision detection between any two, non-adjacent links: (P_iP_i+1) vs. (P_jP_j+1).

The question: it's highly recommended in all works treating this subject of collision detection to use a broad phase and to implement it via a bounding volume hierarchy. For a chain made out of P_i nodes, it can look like this:

I imagine the big blue sphere to contain all links, the green half of them, the reds a quarter and so on (the picture is not accurate, but it's there to help understand the question). What I do not understand is:

How can such a hierarchy speed up computations between segments collision pairs if one has to update it for a deformable linear object such as a chain/wire/etc. each frame? More clearly, what is the actual principle of collision detection broad phases in this particular case/ how can it work when the actual computation of bounding spheres is in itself a time consuming task and has to be done (since the geometry changes) in each frame update? I think I am missing a key point - if we look at the picture where the chain is in a spiral pose, we see that most spheres are already contained within half of others or do intersect them.. it's odd if this is the way it should work.