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The MIPS (maximum inner product search), which finds the item with thehighest inner product with a given query user, is an essential problem in therecommendation field. It is usual that e-commerce companies face situationswhere they want to promote and sell new or discounted items. In thesesituations, we have to consider a question: who are interested in the items andhow to find them? This paper answers this question by addressing a new problemcalled reverse maximum inner product search (reverse MIPS). Given a queryvector and two sets of vectors (user vectors and item vectors), the problem ofreverse MIPS finds a set of user vectors whose inner product with the queryvector is the maximum among the query and item vectors. Although the importanceof this problem is clear, its straightforward implementation incurs acomputationally expensive cost. We therefore propose Simpfer, a simple, fast,and exact algorithm for reverse MIPS. In an offline phase, Simpfer builds asimple index that maintains a lower-bound of the maximum inner product. Byexploiting this index, Simpfer judges whether the query vector can have themaximum inner product or not, for a given user vector, in a constant time.Besides, our index enables filtering user vectors, which cannot have themaximum inner product with the query vector, in a batch. We theoreticallydemonstrate that Simpfer outperforms baselines employing state-of-the-art MIPStechniques. Furthermore, our extensive experiments on real datasets show thatSimpfer is at least two orders magnitude faster than the baselines.

Reverse Maximum Inner Product Search: How to efficiently find users who would like to buy my item?