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arXiv · 2605.22690

Maximum-Weight Two Boxes Symmetric Difference Problem

José Fernández Goycoolea·Luis H. Herrera·Pablo Pérez Lantero·Carlos Seara
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Abstract

Let $P$ be a set of $n$ points in the plane, where each element of $P$ is assigned a weight $\omega(p)$, positive or negative. In this paper, we present an algorithm that runs in $O(n^4\log n)$ time and $O(n)$ space to find two possibly overlapping axis-aligned rectangles $A$ and $B$ so as to maximize the total weight of the points contained in the symmetric difference of $A$ and $B$. The same optimization framework can easily be adapted to solve related problems such as to maximize the total weight in the symmetric difference of $k \geq 3$ boxes and/or in the union of $k \geq 2$ boxes.

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José Fernández Goycoolea, Luis H. Herrera, Pablo Pérez Lantero, Carlos Seara. 2026-05-21. Maximum-Weight Two Boxes Symmetric Difference Problem. https://arxiv.org/abs/2605.22690

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