Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
The Point Hyperplane Cover problem in ℝd takes as input a set of n points in ℝd and a positive integer k. The objective is to cover all the given points with a set of at most k hyperplanes. The D-Polynomial Points Hitting Set (D-Polynomial Points HS) problem in ℝd takes as input a family F of D-degree polynomials from a vector space R in ℝd, and determines whether there is a set of at most k points in ℝd that hit all the polynomials in F. For both problems, we exhibit tight kernels where k is the parameter.
Boissonnat, Jean Daniel; Dutta, Kunal; Ghosh, Arijit; and Kolay, Sudeshna, "Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set" (2018). Conference Articles. 163.