Warm-up:When Luby meets Glauber starting from an arbitrary Xo E [g] at each step,for each vertex vV: GV,E) independently sample a random Luby number B.∈[0,1]； step if B,is locally maximum among its neighborhood Nv): resample X(v)according to the Glauber step marginal distribution induced by u at vertex v conditioning on X(Nv)); Luby step:Independently sample a random independent set. Glauber step:For independent set vertices,update correctly according to the current marginal distributions. Stationary distribution:the Gibbs distribution u.Warm-up: When Luby meets Glauber G(V,E): resample X(v) according to the marginal distribution induced by µ at vertex v conditioning on Xt(N(v)); at each step, for each vertex v∈V: starting from an arbitrary X0 ∈ [q]V independently sample a random number βv∈[0,1]; if βv is locally maximum among its neighborhood N(v): Luby step Glauber step • Luby step: Independently sample a random independent set. • Glauber step: For independent set vertices, update correctly according to the current marginal distributions. • Stationary distribution: the Gibbs distribution µ