@article{4090,
abstract = {In this paper we study the problem of polygonal separation in the plane, i.e., finding a convex polygon with minimum number k of sides separating two given finite point sets (k-separator), if it exists. We show that for k = Θ(n), is a lower bound to the running time of any algorithm for this problem, and exhibit two algorithms of distinctly different flavors. The first relies on an O(n log n)-time preprocessing task, which constructs the convex hull of the internal set and a nested star-shaped polygon determined by the external set; the k-separator is contained in the annulus between the boundaries of these two polygons and is constructed in additional linear time. The second algorithm adapts the prune-and-search approach, and constructs, in each iteration, one side of the separator; its running time is O(kn), but the separator may have one more side than the minimum.},
author = {Herbert Edelsbrunner and Preparata, Franco P},
journal = {Information and Computation},
number = {3},
pages = {218 -- 232},
publisher = {Elsevier},
title = {{Minimum polygonal separation}},
doi = {10.1016/0890-5401(88)90049-1},
volume = {77},
year = {1988},
}