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arXiv · 1610.07999

Rapid Mixing of Hypergraph Independent Set

Jonathan Hermon·Allan Sly·Yumeng Zhang
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Abstract

We prove that the the mixing time of the Glauber dynamics for sampling independent sets on $n$-vertex $k$-uniform hypergraphs is $O(n\log n)$ when the maximum degree $Δ$ satisfies $Δ\leq c 2^{k/2}$, improving on the previous bound [BDK06] of $Δ\leq k-2$. This result brings the algorithmic bound to within a constant factor of the hardness bound of [BGG+16] which showed that it is NP-hard to approximately count independent sets on hypergraphs when $Δ\geq 5 \cdot 2^{k/2}$.

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Jonathan Hermon, Allan Sly, Yumeng Zhang. 2019-12-24. Rapid Mixing of Hypergraph Independent Set. https://doi.org/10.1002/rsa.20830

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