# Multivariate Analysis for Computing Maxima in High Dimensions

## TL;DR

This paper introduces a new algorithm for computing the Maxima of high-dimensional point sets that adapts to input structure, significantly improving performance for dimensions four and above.

## Contribution

It presents a structure-sensitive algorithm that enhances the running time for Maxima computation in high dimensions, surpassing previous solutions.

## Key findings

- Improved algorithm for d ≥ 4 dimensions
- Runs faster on structured input sets
- Outperforms existing methods for high-dimensional Maxima

## Abstract

We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher dimensions there is still room for improvements. We present an algorithm sensitive to the structural entropy of the input set, which improves the running time, for large classes of instances, on the best solution for \textsc{Maxima} to date for $d \ge 4$.