(color online) Numerical results for random directed networks. α, arc density; ρ, fraction of feedback arcs. Algorithmic results of the local DH (circles), BPD (pluses), and SA (crosses) are compared with the predictions of the RS mean-field theory (triangles). Level upper-bound D = 200 and inverse temperature for the BPD algorithm and the RS theory. Each data point is the average over 40 network instances of size ; standard deviation (not shown) is less than . Four ensembles of random networks are considered: (a) Erdös–Rényi (ER); (b) regular random (RR); (c) scale-free static (SFS^[33]) with in- and out-degree exponents and ; and (d) scale-free configurational (SFC^[32]) with in-degree exponent and different out-degree exponents and minimum in- and out-degree and in- and out-degree upper-bound .