Abstract:A family S of convex sets in the plane defines a hypergraph H = (S, E) as
follows. Every subfamily S' of S defines a hyperedge of H if and only if there
exists a halfspace h that fully contains S' , and no other set of S is fully
contained in h. In this case, we say that h realizes S'. We say a set S is
shattered, if all its subsets are realized. The VC-dimension of a hypergraph H
is the size of the largest shattered set. We show that the VC-dimension for
pairwise disjoint convex sets in the plane is bounded b… Show more
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