An optimal algorithm for finding an enclosing planar rectilinear annulus of minimum width

Location Science

“…There is also a relation to equity problems (see Gluchshenko 2008;Drezner and Drezner 2007) of point facility location and to a problem in computational geometry which is to find an annulus of smallest width. These relations are specified in Sect.…”

“…Its rectangular version is due to Gluchshenko et al (2009). In R D the Euclidean minmax hypersphere location problem has been analyzed mainly in the Euclidean case, see Nievergelt (2002).…”

“…We conclude that minmax hypersphere location problems can be interpreted as ordered median point location problems. Therefore, the point x may be interpreted as a fair location for a service facility as used in equity problems, see Gluchshenko (2008) for further results.…”

“…Gluchshenko (2008) and Gluchshenko et al (2009) consider the minimal annulus problem for the rectangular distance. This means, the circle to be located is a diamond, and the distances from the given points to the circle are measured in the rectangular norm.…”

“…Theorem 7.13 (FDS for the Rectangular Minmax Circle) (Gluchshenko et al 2009) There exists a minmax circle whose center point is a center point of a smallest enclosing square.…”