Figure 5

Influence of different parameter settings in the cost functional. Example with the three sets A = {1, 2, 3}, B = {2, 4, 5}, and C = {3, 4, 6} such that there is a pairwise overlap of one element, but not among all three sets, i.e. |A ∩ B| = |A ∩ C| = |B ∩ C| = 1 and |A ∩ B ∩ C| = 0. That means no perfect solution satisfying all constraints can be found, but only approximate ones, which are influenced by the relative weighting of the partial costs. The left diagram shows the settings α = 0 and β = γ = 1 so that unwanted intersections (the gray area in the middle) are ignored. For the diagram on the right, a was set to 50, thus showing a smaller gray area at the expense of a larger area deviation.