Reduction from Max-Weight k-Clique to Max-Weight Rectangle

FROM: Max-Weight k-Clique TO: Max-Weight Rectangle

Implications

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 $k=\lceil d^{2}\epsilon^{-1}\rceil$

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