Oblivious Setmaxima for Intersection of Convex Polygons
Abstract
In this paper we revisit the well known setmaxima 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 setmaxima 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 nontrivial 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 DOI:
 10.48550/arXiv.1811.02676
 arXiv:
 arXiv:1811.02676
 Bibcode:
 2018arXiv181102676B
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 11 pages