Separated high-density points and valley detection on polynomial densities are ∃R-complete; connected components and hole detection are ∃R-hard, giving the first exact classification of continuous clustering in the real polynomial hierarchy.
Fixed points, nash equilibria, and the existential the- ory of the reals
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
verdicts
UNVERDICTED 2representative citing papers
Order type realizability, ∃R-complete in the worst case, can be decided in expected NP time under smoothed analysis.
citing papers explorer
-
How Hard Is Continuous Clustering? Lower Bounds from the Existential Theory of the Reals
Separated high-density points and valley detection on polynomial densities are ∃R-complete; connected components and hole detection are ∃R-hard, giving the first exact classification of continuous clustering in the real polynomial hierarchy.
-
Smoothed Analysis of Order Types
Order type realizability, ∃R-complete in the worst case, can be decided in expected NP time under smoothed analysis.