Geoscience Reference
In-Depth Information
Concerning the location of new types of dimensional structures, researchers
should look for shapes which are of interest for other disciplines or for applications.
Similarly, identifying additional restrictions and particularities arising in applica-
tions in operations research, statistics, and computational geometry and including
them in the models is a future challenge.
Acknowledgements
I want to thank Robert Schieweck for providing useful hints on line and
hyperplane location problems.
References
Agarwal P, Efrat A, Sharir M, Toledo S (1993) Computing a segment center for a planar point set.
J Algorithm 15:314-323
Agarwal P, Aronov B, Peled S, Sharir M (1999) Approximation and exact algorithms for minimum-
width annuli and shells. In: Proceedings of the 15th ACM symposium on computational
geometry, pp 380-389
Agarwal P, Peled SH, Varadarajan K (2004) Approximation extent measures of points. J ACM
51:605-635
Alonso J, Martini H, Spirova M (2012a) Minimal enclosing discs, circumcircles, and circumcenters
in normed planes (part I). Comput Geom Theor Appl 45:258-274
Alonso J, Martini H, Spirova M (2012b) Minimal enclosing discs, circumcircles, and circumcenters
in normed planes (part II). Comput Geom Theor Appl 45:350-369
Bennet K, Mangasarian O (1992) Robust linear programming discrimination of two linearly
inseparable sets. Optim Method Softw 1:23-34
Bertsimas D, Shioda R (2007) Classification and regression via integer optimization. Oper Res
55:252-271
Blanquero R, Carrizosa E, Hansen P (2009) Locating objects in the plane using global optimization
techniques. Math Oper Res 34:837-858
Blanquero R, Carrizosa E, Schöbel A, Scholz D (2011) Location of a line in the three-dimensional
space. Eur J Oper Res 215:14-20
Brimberg J, Nickel S (2009) Constructing a DC decomposition for ordered median problems. J
Global Optim 45:187-201
Brimberg J, Wesolowsky G (2000) Note: facility location with closest rectangular distances. Nav
Res Log 47:77-84
Brimberg J, Juel H, Schöbel A (2002) Linear facility location in three dimensions - models and
solution methods. Oper Res 50:1050-1057
Brimberg J, Juel H, Schöbel A (2003) Properties of 3-dimensional line location models. Ann Oper
Res 122:71-85
Brimberg J, Juel H, Schöbel A (2009a) Locating a circle on the plane using the minimax criterion.
Stud Locat Anal 17:46-60
Brimberg J, Juel H, Schöbel A (2009b) Locating a minisum circle in the plane. Discrete Appl Math
157:901-912
Brimberg J, Juel H, Körner MC, Schöbel A (2011a) Locating a general minisum 'circle' on the
plane. 4OR-Q J Oper Res 9:351-370
Brimberg J, Juel H, Körner MC, Schöbel A (2011b) Locating an axis-parallel rectangle on a
Manhattan plane. TOP 22:185-207
Brimberg J, Juel H, Körner MC, Schöbel A (2013a) On models for continuous facility location
with partial coverage. J Oper Res Soc. doi:JORS.2013.142
