Online algorithms achieve multiplicative approximation r^{1/(r-1)} for maximum independent sets in dense r-uniform ER hypergraphs and (max γ_i)^{-1/(r-1)} for balanced sets in r-partite versions, with matching lower bounds.
The Average-Case Complexity of Counting Cliques in Erd¨ os-R´ enyi Hypergraphs
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Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs
Online algorithms achieve multiplicative approximation r^{1/(r-1)} for maximum independent sets in dense r-uniform ER hypergraphs and (max γ_i)^{-1/(r-1)} for balanced sets in r-partite versions, with matching lower bounds.