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  "path": "/abs/2605.22690v1",
  "publishedAt": "2026-05-22T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "José Fernández Goycoolea",
    "Luis H. Herrera",
    "Pablo Pérez Lantero",
    "Carlos Seara"
  ],
  "textContent": "**Authors:** José Fernández Goycoolea, Luis H. Herrera, Pablo Pérez Lantero, Carlos Seara\n\nLet $P$ be a set of $n$ points in the plane, where each element of $P$ is assigned a weight $ω(p)$, 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.",
  "title": "Maximum-Weight Two Boxes Symmetric Difference Problem"
}