Properties of Three-Dimensional Median Line Location Models

Annals of Operations Research

Volumn 122, Issue 1-4, 2003, Pages 71-85

  Brimberg, Jack ^a   Juel, Henrik ^b   Schöbel, Anita ^c  

^a ROYAL MILITARY COLLEGE OF CANADA   (Canada)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c University of Koblenz Landau   (Germany)

Author keywords

Continuous location; Linear facility; Three dimensions

Indexed keywords

EID: 0347756755     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/A:1026138205325     Document Type: Article

References (20)

1. Brazil, M., D.H. Lee, J.H. Rubinstein, D.A. Thomas, J.F. Weng, and N.C. Wormald. (2001). "Network Optimisation of Underground Mine Designs." Submitted to AusIMM Proceedings.
2. Brimberg, J., H. Juel, and A. Schöbel. (2002). "Linear Facility Location in Three Dimensions - Models and Solution Methods." Operations Research 50(6), 1050-1057.
3. p Distances." Operations Research 41, 1153-1163.
4. Brimberg, J., R. Chen, and D. Chen. (1998). "Accelerating Convergence in the Fermat-Weber Location Problem." Operations Research Letters 22, 151-157.
5. Díaz-Báñez, J.M., J.A. Mesa, and A. Schöbel. (2002). "Continuous Location of Dimensional Structures." Report in Wirtschaftsmathematik 79/2002, University of Kaiserslautern.
6. Follert, F. (1995). "Maxmin Location of an Anchored Ray in 3-Space and Related Problems." In 7th Canadian Conference on Computational Geometry, Quebec.
7. Follert, F., E. Schömer, J. Sellen, M. Smid, and C. Thiel. (1995). "Computing a Largest Empty Anchored Cylinder and Related Problems." Technical Report MPI-91-1-001, Max-Planck-Institut für Informatik, Saarbrücken.
8. Houle, M.E. and G.T. Toussaint. (1988). "Computing the Width of a Set." IEEE Transactions on Pattern Analysis and Machine Intelligence 10, 760-765.
9. Korneenko, N.M. and H. Martini. (1993). "Hyperplane Approximation and Related Topics." In J. Pach (ed.), New Trends in Discrete and Computational Geometry. New York: Springer.
10. Martini, H. and A. Schöbel. (1998). "Median Hyperplanes in Normed Spaces - A Survey." Discrete Applied Mathematics 89, 181-195.
11. Martini, H. and A. Schöbel. (1999). "A Characterization of Smooth Norms." Geometriae Dedicata, 77 173-183.
12. Minkowski, H. (1967). Gesammelte Abhandlungen. New York: Chelsea.
13. Morris, J.G. and J.P. Norback. (1980). "A Simple Approach to Linear Facility Location." Transportation Science 14, 1-8.
14. Morris, J.G. and J.P. Norback. (1983). "Linear Facility Location - Solving Extensions of the Basic Problem." European Journal of Operational Research 12, 90-94.
15. Norback, J.P. and J.G. Morris. (1980). "Fitting Hyperplanes by Minimizing Orthogonal Deviations." Mathematical Programming 19, 102-105.
16. Schöbel, A. (1998). "Locating Least Distant Lines in the Plane." European Journal of Operational Research 106(1), 152-159.
17. Schöbel, A. (1999). Locating Lines and Hyperplanes: Theory and Algorithms. Dordrecht: Kluwer.
18. Schömer, E., J. Sellen, M. Teichmann, and C. Yap. (1996). "Efficient Algorithms for the Smallest Enclosing Cylinders Problem." In Proceedings of the 8th Canadian Conference on Computational Geometry.
19. Wesolowsky, G.O. (1975). "Location of the Median Line for Weighted Points." Environment and Planning A 7, 163-170.
20. Zemel, E. (1984). "An O(n) Algorithm for the Linear Multiple Choice Knapsack Problem and Related Problems." Information Processing Letters 18, 123-128.