A Moser-Tardos style algorithm [Feng,Vishnoi,Y.'19] Gibbs distribution:u(o)cxΠAe(ooo,)Ib,(a） e={u,v}∈E v∈V current sample:Xu R←-{v∈V|v is updated or incident to updated e; while R≠odo for every vE R,resample X~b,independently; every internal e={u,v)CR accepts ind.w.p.A(X); every boundary e={u,v}with uR,vR accepts ind.w.p. A(,X) A(Xold,X) /Xold:X before resampling R← e; e rejectsA Moser-Tardos style algorithm ; while do for every , resample independently; every internal accepts ind. w.p. ; every boundary with accepts ind. w.p. ; R ← {v ∈ V ∣ v is updated or incident to updated e} R ≠ ∅ v ∈ R Xv ∼ bv e = {u, v} ⊆ R Ae(Xu, Xv) e = {u, v} u ∈ R, v ∉ R R ← ⋃ e rejects e // X : before resampling ��� ∝ u Xu Ae(Xu, Xv) Ae(X��� u , Xv) ; Gibbs distribution: μ(σ) ∝ ∏ e={u,v}∈E Ae (σu, σv)∏ v∈V bv (σv) current sample: X ∼ μ [Feng, Vishnoi, Y. ’19]