Our Results:Uniform Distribution ·CSP instanceΦ=(V,C)with solution set∑ Each variable v has uniform distribution over Individual falsifying probability:p max Pr[c is False] ·Degree:△=max#{c'∈C|vbl(c)nvbl(c)≠0} ·lfp0.175.△≤1，then we can Beats 0.142 from [JPV'20] Matches 0.175 for k-CNF formula from [JPV'21] ·sample uniform random o∈∑ ·in expected O(n log n) Indeed k-CNF case is our bottleneck If each is large enough,it can be improved to p2/3.△s1 Hypergraph coloringOur Results: Uniform Distribution • CSP instance Φ = 𝑉,𝐶 with solution set Σ • Each variable 𝑣 has uniform distribution over Ω𝑣 • Individual falsifying probability: 𝑝 = max 𝑐∈𝐶 Pr[𝑐 is 𝐅𝐚𝐥𝐬𝐞] • Degree: Δ = max 𝑐∈𝐶 # 𝑐 ′ ∈ 𝐶 vbl 𝑐 ∩ vbl 𝑐 ′ ≠ ∅ • If 𝑝 0.175 ⋅ Δ ≲ 1, then we can • sample uniform random 𝜎 ∈ Σ • in expected 𝑂 𝑛 log 𝑛 Beats 0.142 from [JPV’20] Matches 0.175 for 𝑘-CNF formula from [JPV’21] Indeed 𝑘-CNF case is our bottleneck If each Ω𝑣 is large enough, it can be improved to 𝑝 1/3 ⋅ Δ ≲ 1 Hypergraph coloring