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army1987 comments on Relative Configuration Space - Less Wrong
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Comments (21)
When you take into account that d(A, A) = 0 and d(A, B) = d(B, A), you only need N(N - 1)/2 distances.
You'd never even fewer in a flat 3D space, but if the particles can be in an arbitrarily curved space I think you need all of those.
N(N-1)/2 is O(N^2), which is not substantially better. Particularly to the soul of a computer scientist, which largely ignores constant factors anyway.