Improved Algorithm for Computing the Maximum-volume Bichromatic Separating Box

TL;DR

This paper presents an improved algorithm for finding the maximum-volume bichromatic separating box in 3D point sets, reducing the computational complexity from previous methods.

Contribution

The authors develop a more efficient algorithm with a time complexity of O(m^2 + n), improving upon the prior O(m^2 (m + n)) approach.

Findings

The new algorithm significantly reduces computation time.

It maintains accuracy in identifying the maximum-volume separating box.

The approach is scalable for larger datasets.

Abstract

We consider the problem of computing the largest-area bichromatic separating box among a set of $n$ red points and a set of $m$ blue points in three dimensions. Currently, the best-known algorithm to solve this problem takes $O(m^2 (m + n))$ time and $O(m + n)$ space. In this paper, we come up with an improved algorithm for the problem, which takes $O(m^2 + n)$ time.