Counting hypergraph colorings in the local lemma regime

11/09/2017

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by   Heng Guo, et al.

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We give a fully polynomial-time approximation scheme (FPTAS) to count the number of q-colorings for k-uniform hypergraphs with maximum degree Δ if k> 28 and q > 315Δ^14/k-14. We also obtain a polynomial-time almost uniform sampler if q> 798Δ^16/k-16/3. These are the first approximate counting and sampling algorithms in the regime q≪Δ (for large Δ and k) without any additional assumptions. Our method is based on the recent work of Moitra (STOC, 2017). One important contribution of ours is to remove the dependency of k and Δ in Moitra's approach.