Smaller Kernels for Hitting Set Problems of Constant Arity

We demonstrate a kernel of size O(k2) for 3-Hitting Set (Hitting Set when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Trotter linear-size kernel for Vertex Cover, and generalizes to demonstrating a kernel of size O(kr − − 1) for r-Hitting Set (for fixed r).