Minimum-width rectangular annulus

Geometric separability using orthogonal objects

“…Gluchshenko et al [11] gave an O(n log n) algorithm to compute a minimum width enclosing rectilinear annulus. Mukherjee et al [15] gave an O(n) algorithm that computes minimum width enclosing axis-parallel rectangular annulus and an O(n 2 log n) algorithm that computes minimum width enclosing rectangular annulus in arbitrary orientation. Bae [1] gave an algorithm that runs in O(n 3 log n) time that computes the minimum width enclosing square annulus.…”

“…If R in contains blue points inside, then a separating rectangular annulus does not exist. If R is empty, then the problem can be solved by the algorithm that computes the minimum width enclosing rectangular annulus given in [15]. Lemma 1.…”

Minimum-width double-strip and parallelogram annulus

“…If one considers rectangular or square annuli in arbitrary orientation, the problem becomes more difficult. Mukherjee et al [12] presented an O(n 2 log n)-time algorithm that computes a minimum-width rectangular annulus in arbitrary orientation and arbitrary aspect ratio. The author [5] showed that a minimum-width square annulus in arbitrary orientation can be computed in O(n 3 log n) time, and recently improved it to O(n 3 ) time [6].…”

Computing a Minimum-Width Cubic and Hypercubic Shell

“…If one considers rectangular or square annuli in arbitrary orientation, the problem gets more difficult. Mukherjee et al [11] presented an O(n 2 log n)-time algorithm that computes a minimum-width rectangular annulus in arbitrary orientation and arbitrary aspect ratio. The author [5] recently showed that a minimum-width square annulus in arbitrary orientation can be computed in O(n 3 log n) time.…”

“…For d ≥ 3, the d-dimensional generalization of annuli is often referred to shells of a certain body of volume. Mukherjee et al [11] showed that a minimum-width shell of d-dimensional axis-parallel boxes (or hyper-rectangules) can be computed in O(dn) time. For the minimum-width spherical or hyperspherical shells, Chan [8] showed an O(n d/2 +1 )-time exact algorithm, and some approximation algorithms are known [4,8].…”