Reduction from Max-Weight K-Clique to Weighted Depth

FROM: Max-Weight K-Clique TO: Weighted Depth

Implications

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 $k=d$

Year

2016

Reference

Backurs, Arturs, Nishanth Dikkala, and Christos Tzamos. "Tight Hardness Results for Maximum Weight Rectangles}}." 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Vol. 55. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2016.

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