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

arXiv: https://arxiv.org/abs/2110.07131 · HTML: https://mlsanity.com/paper/2110.07131/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2021.

## Built on by (most cited first, 5 of 5)

- [A Theoretical Analysis Of Nearest Neighbor Search On Approximate Near Neighbor Graph](https://mlsanity.com/paper/2303.06210/) (2023)
- [Faster Maximum Inner Product Search in High Dimensions](https://mlsanity.com/paper/2212.07551/) (2022)
- [SAH: Shifting-aware Asymmetric Hashing for Reverse k-Maximum Inner Product Search](https://mlsanity.com/paper/2211.12751/) (2022)
- [Bypassing the Popularity Bias: Repurposing Models for Better Long-Tail Recommendation](https://mlsanity.com/paper/2410.02776/) (2024)
- [An adaptive subsampling method for large-sample feature screening](https://mlsanity.com/paper/2509.16085/) (2025)

## Abstract (arXiv)

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