The following observation provides the idea to how to determine the maximal cliques with lowest semi-square r (t): Each point x ∈ r (t) is overlapped by a set of rectangles from Pr(t) ⋃ Qr(t) ⋃ Rr(t). The crucial observation is that their corresponding semi-squares are also pairwise intersecting, so x ∈ r (t) denotes a clique of semi-squares. This is important, because we state here that in the restriction to r (t) we have an equivalence between the intersection of the rectangles and the intersection of the semi-squares. Thus, the question to finding maximal cliques in the c-max-tolerance graph is now reduced to finding an area where a maximal set of rectangles intersects.