Weighted Depth

Description

Given a set of $n$ weighted axis-parallel boxes in $d$-dimensional space $\mathbb{R}^d$, find a point $p \in \mathbb{R}^d$ that maximizes the sum of the weights of the boxes containing $p$.

Related Problems

Related: Strips Cover Box, Triangles Cover Triangle, Hole in Union, Triangle Measure, Point Covering, Max-Weight Rectangle

Parameters

$n$: number of boxes

$d$: 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: $O(n^{\lfloor d/{2}\rfloor-\epsilon})$ for $N$ weighted axis-parallel boxes in $\mathbb{R}^d$ then: from-time: $O(n^{k-{2}\epsilon})$ on $n$ vertex graphs for $k=d$	2016	https://arxiv.org/pdf/1602.05837.pdf	link

References/Citation

https://doi.org/10.1109/FOCS.2013.51

https://arxiv.org/pdf/1602.05837.pdf