Högskolan i Skövde

Given a set S of subsets of a reference set X, we define the problem of finding c subsets of X that maximize the size of the intersection among the included subsets. Maximizing the size of the intersection means that they are subsets of the sets in S and they are as large as possible. We can understand the result of this problem as c consensus sets of S, or c consensus representatives of S. From the perspective of lattice theory, each representative will be a meet of some sets in S. In this paper we define formally this problem, and present heuristic algorithms to solve it. We also discuss the relationship with other established problems in the literature.