Maximum-Width Empty Square and Rectangular Annulus

Abstract

An annulus is, informally, a ring-shaped region, often described by two concentric circles. The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of n points in the plane. This problem can also be interpreted as the problem of finding an optimal location of a ring-shaped obnoxious facility among the input points. In this paper, we study square and rectangular variants of the maximum-width empty anuulus problem, and present first nontrivial algorithms. Specifically, our algorithms run in \(O(n^3)\) and \(O(n^2 \log n)\) time for computing a maximum-width empty axis-parallel square and rectangular annulus, respectively. Both algorithms use only O(n) space.