Year: 2026
Type: preprint
Abstract: We present a new upper bound on the defect of the Mondrian Art Problem. The Mondrian Art Problem asks for a partition of an $n \times n$ square with rectangles of distinct dimensions such that the difference (defect) between the largest and smallest rectangle areas is minimized. We prove that for any $n \times n$ square, there exists a partition with defect $O(n^{5/6})$, improving upon the previously conjectured $O (n/\log n)$ upper bound. We also implement an algorithm that provides empirical evidence supporting our theoretical bound.
Source: arXiv (Cornell University)
Institutions: University of Florida, Carnegie Mellon University
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207555662