  In this paper we revisit the well known set-maxima problem in the oblivious
setting. Let $X=\{x_1,\ldots, x_n\}$ be a set of $n$ elements with an
underlying total order. Let $\mathcal{S}=\{S_1,\ldots,S_m\}$ be a collection of
$m$ distinct subsets of $X$. The set-maxima problem asks to determine the
maxima of all the sets in the collection. In the comparison tree model we are
interested in determining the number of comparisons necessary and sufficient to
solve the problem. We present an oblivious algorithm based on the lattice
structure of the input set system. Our algorithm is simple and yet for many set
systems gives a non-trivial improvement over known deterministic algorithms. We
apply our algorithm to a special $\cal S$ which is determined by an
intersection structure of convex polygons and show that $O(n)$ comparisons
suffice.
