Tight Hardness Results for Maximum Weight Rectangles

@article{Backurs2016TightHR,
  title={Tight Hardness Results for Maximum Weight Rectangles},
  author={A. Backurs and Nishanth Dikkala and Christos Tzamos},
  journal={ArXiv},
  year={2016},
  volume={abs/1602.05837}
}
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… Expand
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