Fig. 6

Performance of partitioning methods for minimizing \(c(\vec {G},{\mathcal {V}})\) on perturbed BMGs \((\vec {G},\sigma )\). The rows correspond to different insertion and deletion probabilities (indicated in the l.h.s. panels) used to disturb the original BMGs. The l.h.s. panels show the distribution of the no. of arc modifications in total, arc insertions and arc deletions of the disturbed digraphs w.r.t. the original BMGs. The r.h.s. panels show the distribution of UR-costs \(c(\vec {G},{\mathcal {V}})\) (red) obtained for each method, and of the no. of arcs in \(U_1(\vec {G},{\mathcal {V}})\), \(U_2(\vec {G},{\mathcal {V}})\), and \(U_3(\vec {G},{\mathcal {V}})\) (i.e., the sets that contribute to the UR-cost). Example plot for \(|V|=30\) vertices and \(|\sigma (V)|=10\) colors in each digraph. Among the 200 generated digraphs, only those with a connected Aho graph \([{\mathcal {R}}(\vec {G},\sigma ), V(\vec {G})]\) are included in each of the five rows (93%, 100%, 100%, 60%, 95%)