Parameterized Query Complexity of Hitting Set Using Stability of Sunflowers

In this paper, we study the query complexity of parameterized decision and optimization versions of Hitting-Set. We also investigate the query complexity of Packing. In doing so, we use generalizations to hypergraphs of an earlier query model, known as BIS introduced by Beame et al. in ITCS\u2718. The query models considered are the GPIS and GPISE oracles. The GPIS and GPISE oracles are used for the decision and optimization versions of the problems, respectively. We use color coding and queries to the oracles to generate subsamples from the hypergraph, that retain some structural properties of the original hypergraph. We use the stability of the sunflowers in a non-trivial way to do so