Group control for consent rules with consecutive qualifications

We study group control for consent rules in the setting of group identification restricted to domains of consecutive qualifications. In particular, these domains are equivalent to the (0,1)-matrix corresponding to an input opinion profile being either row circular or column circular. By utilizing two ILPs, we show that these decision problems, being NP-hard in general, become polynomial-time solvable under these restrictions. We also derive combinatorial algorithms for more special cases and for consent rules with one of the consent quotas being equal to one.