Max-Weight Rectangle (Geometric Covering Problems)
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Description
Given $n$ weighted points (positive or negative) in $d \geq 2$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains?
Related Problems
Related: Strips Cover Box, Triangles Cover Triangle, Hole in Union, Triangle Measure, Point Covering, Weighted Depth
Parameters
$n$: number of points
$d$: dimensionality of space
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Max-Weight k-Clique | if: to-time: $O(N^{d-\epsilon})$ on $N$ weighted points in $d$ dimensions then: from-time: $O(n^{k-\epsilon})$ on $n$ vertices, where $k=\lceil d^{2}\epsilon^{-1}\rceil$ |
2016 | https://arxiv.org/pdf/1602.05837.pdf | link |
References/Citation
https://doi-org.ezproxy.canberra.edu.au/10.1016/j.ipl.2014.03.007