What is the $NP$ problem whose status in $P$ or $NP$-complete is still unsettled, as of 2018?
This question is inspired by the following two recent breakthroughs:
- The work of Mulzer et. al on $NP$-completeness of min-weight triangulation.
- Recent quasi-polynomial algorithm of Babai for graph isomorphism. The link is to Helfgott's more recent (2017) paper.