The Set-Maxima Problem in a Geometric Setting.

In this paper we look at the classical set-maxima problem. We give a new result using a sparse lattice of subsets. We then extend this to a geometric setting. Let $P$ be a set of $n$ points in a plane and $mathcal{S}$ be a set of convex regions. Let a key value be assigned to each point. The problems is to determine for each convex region of $mathcal{S}$ the point having the largest key. We give a parameterized result for the comparison complexity.