# To Index or Not to Index: Optimizing Exact Maximum Inner Product Search

## TL;DR

This paper introduces MAXIMUS, a hardware-efficient MIPS solver, and OPTIMUS, a data-dependent optimizer that selects the best solver for each input, significantly outperforming existing methods.

## Contribution

The paper presents MAXIMUS and OPTIMUS, novel solutions that improve exact MIPS search efficiency and adaptively select the best method based on input data.

## Key findings

- MAXIMUS outperforms state-of-the-art solvers for some inputs.
- OPTIMUS effectively chooses the best solver for each input with minimal overhead.
- Combined, they achieve up to 10.9× speedup on MIPS datasets.

## Abstract

Exact Maximum Inner Product Search (MIPS) is an important task that is widely pertinent to recommender systems and high-dimensional similarity search. The brute-force approach to solving exact MIPS is computationally expensive, thus spurring recent development of novel indexes and pruning techniques for this task. In this paper, we show that a hardware-efficient brute-force approach, blocked matrix multiply (BMM), can outperform the state-of-the-art MIPS solvers by over an order of magnitude, for some -- but not all -- inputs. In this paper, we also present a novel MIPS solution, MAXIMUS, that takes advantage of hardware efficiency and pruning of the search space. Like BMM, MAXIMUS is faster than other solvers by up to an order of magnitude, but again only for some inputs. Since no single solution offers the best runtime performance for all inputs, we introduce a new data-dependent optimizer, OPTIMUS, that selects online with minimal overhead the best MIPS solver for a given input. Together, OPTIMUS and MAXIMUS outperform state-of-the-art MIPS solvers by 3.2$\times$ on average, and up to 10.9$\times$, on widely studied MIPS datasets.