Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems.
However, efficient algorithms exist to speed up MIPS search.
[1][2] Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem.
[3] Like other forms of NNS, MIPS algorithms may be approximate or exact.
[4] MIPS search is used as part of DeepMind's RETRO algorithm.