Algorithms for diversity and clustering in social networks through dot product graphs

We also consider the situation when two individuals u and v are connected if and only if their preferences are not antithetical, that is, if and only if au·av≥0, and the situation when two individuals u and v are connected if and only if their preferences are neither antithetical nor “orthogonal”, that is, if and only if au·av>0. For these two cases we prove that the diversity problem is polynomial-time solvable for any fixed d and that the clustering problem is polynomial-time solvable for d ≤ 3.