Perfect Sampling vs Approximate Sampling ·D1 is uniform over{1,2,…,n} .D2 is uniform over {1,2,...,n-vn} .The total variation distance between Dand D is=o(1) Fairness:all solutions are created equal! Indeed the case for [FGYZ'20,FHY'20,JPV'21] Some solutions are never outputted Solutions inherently hard to find?Perfect Sampling vs Approximate Sampling • 𝐷1 is uniform over 1,2, … , 𝑛 • 𝐷2 is uniform over 1,2, … , 𝑛 − 𝑛 • The total variation distance between 𝐷1 and 𝐷2 is 𝑂 1 𝑛 = 𝑜 1 • Fairness: all solutions are created equal! • Indeed the case for [FGYZ’20, FHY’20, JPV’21] • Some solutions are never outputted • Solutions inherently hard to find?