# Tight Hardness Results for Maximum Weight Rectangles

@article{Backurs2016TightHR,
title={Tight Hardness Results for Maximum Weight Rectangles},
author={Arturs Backurs and Nishanth Dikkala and Christos Tzamos},
journal={ArXiv},
year={2016},
volume={abs/1602.05837}
}
• Published 1 February 2016
• Mathematics, Computer Science
• ArXiv
Given $n$ weighted points (positive or negative) in $d$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains? The best known algorithm for this problem is based on a reduction to a related problem, the Weighted Depth problem [T. M. Chan, FOCS'13], and runs in time $O(n^d)$. It was conjectured [Barbay et al., CCCG'13] that this runtime is tight up to subpolynomial factors. We answer this conjecture affirmatively by providing a matching conditional…

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