I stumbled on this problem and I wanna know if there is a better solution. There are $n$ 3d vectors with $x$, $y$, and $z$ components and I wanna find all pairs of perpendicular vectors in this set. Is there any better way than to verify all possible pairs of 3 vectors, some kind of optimization (not the obvious ones)?

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    $\begingroup$ You want to know the better solution, what is your solution? What are obvious optimizations? $\endgroup$ – Evil Sep 10 '19 at 14:29
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    $\begingroup$ I think this is his solution "to verify all possible pairs" @Evil $\endgroup$ – narek Bojikian Sep 10 '19 at 17:18

The problem can be solved in time $\tilde{O}(n^{4/3})$, using several algorithms:

There is an essentially matching lower bound due to Erickson, New lower bounds for Hopcroft's problem. See also Williams and Yu, Finding orthogonal vectors in discrete structures.

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