A multifacility location problem on median spaces

Discrete Applied Mathematics

Volumn 64, Issue 1, 1996, Pages 1-29

  Chepoi, Victor ^a,b  

^a Catedra de Cibernetica Matemat   (Moldova)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039331348     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0166-218X(95)00115-8     Document Type: Article

References (55)

1. M.J. Atallah and D.Z. Chen, Parallel rectilinear shortest path with rectilinear obstacles, Comput. Geom. Theory Appl. 1 (1991) 79-113.
2. F. Aurenhammer and J. Hagauer, Recognizing binary Hamming graphs, Lecture Notes in Computer Science 484 (Springer, Berlin, 1991) 90-98.
3. S.P. Avann, Metric ternary distributive semi-lattices, Proc. Amer. Math. Soc. 12 (1961) 407-414.
4. H.-J. Bandelt, Single facility location on median networks, submitted.
5. H.-J. Bandelt and J.P. Barthelemy, Medians in median graphs, Discrete Appl. Math. 8 (1984) 131-142.
6. 1-embedding of weakly median graphs, in preparation.
7. H.-J. Bandelt and V. Chepoi, Graphs of acyclic cubical complexes, in preparation.
8. H.-J. Bandelt and J. Hedlíková, Median algebras, Discrete Math. 45 (1983) 1-30.
9. J.P. Barthelemy and M.F. Janowitz, A formal theory of consensus, SIAM J. Discrete Math. 4 (1991) 305-322.
10. J.P. Barthelemy, B. Leclerc and B. Monjardet, On the use of ordered sets in problems of comparison and consensus of classifications, J. Classification 3 (1986) 187-224.
11. J.P. Barthelemy and B. Monjardet, The median procedure in cluster analysis and social choice theory, Math. Social Sci. 1 (1981) 235-268.
12. L.M. Blumenthal, Theory and Applications of Distance Geometry (Oxford University Press, London, 1953).
13. A.V. Cabot, R.L. Francis and M.A. Stary, A network flow solution to a rectilinear distance facility location problem, AIIE Trans. 2 (1970) 132-141.
14. B. Chazelle, Triangulating a simple polygon in linear time, Discrete Comput. Geom. 6 (1991) 485-524.
15. V. Chepoi, d-Convex sets in graphs, Dissertation, Moldova State University, Chişinǎu, (1986) (in Russian).
16. V. Chepoi, The generalized Weber problem for discrete median spaces, Kibernetika 1 (1991) 61-69 (in Russian).
17. V. Chepoi and F. Dragan, Computing the median point of a simple rectilinear polygon, Inform. Process. Lett. 49 (1994) 281-285.
18. T.Y. Cheung, Multifacility location problem with rectilinear distance by the minimum-cut approach, ACM Trans. Math. Software 6 (1980) 387-390.
19. 2) time, in: Proceeding of the 3rd Third Annual ACM Symposium on Computational Geometry (1987) 251-257.
20. P.M. Dearing, R.L. Francis and T.J. Lowe, Convex location problems on tree network, Oper. Res. 24 (1976) 628-642.
21. P.M. Dearing and G.J. Langford, The multifacility total location problem on a tree network, Technical Report 209, Department of Mathematical Science Clemson University (1975).
22. M. de Berg, On rectilinear link distance, Comput. Geom. Theory Appl. 1 (1991) 13-34.
23. M. de Berg, M. van Kreveld, B.L. Nilsson and M. Overmars, Shortest path queries in rectilinear worlds, Technical Report RUU-CS-91-20, Department of Computer Science, Utrecht University (1991).
24. P.J. de Rezende, D.T. Lee and Y.F. Wu, Rectilinear shortest paths with rectilinear barriers, Discrete Comput. Geom. 4 (1989) 41-53.
25. E.A. Dinic, Algorithm for solution of a problem of maximum flow in network with power estimation, Soviet Math. Dokl. 11 (1970) 1277-1280.
26. D.Z. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B. 14 (1973) 263-267.
27. A.W.M. Dress and R. Scharlau, Gated sets in metric spaces, Aequationes Math. 34 (1987) 112-120.
28. H. Edelsbrunner, L.J. Guibas and J. Stolfi, Optimal point location in a monotone subdivision, SIAM J. Comput. 15 (1986) 317-340.
29. R.L. Francis and J.A. White, Facility Layout and Location. An Analytical Approach (Prentice-Hall, Englewood Cliffs, NJ, 1974).
30. A.J. Goldman and C.J. Witzgall, A localization theorem for optimal facility placement, Transportation Sci. 4 (1970) 406-409.
31. P. Hansen, D. Peeters and J.F. Thisse, An algorithm for a constrained Weber problem, Management Sci. 28 (1981) 1285-1295.
32. J. Hooker, Nonlinear network location models, Ph.D. Thesis, University of Tennessee (1984).
33. J. Isbell, Median algebra, Trans. Amer. Math. Soc. 260 (1980) 319-362.
34. A.V. Karzanov, Determining the maximal flow in network by the method of preflows, Soviet Math. Dokl. 15 (1974) 434-437.
35. D.G. Kirkpatrick, Optimal search in planar subdivisions, SIAM J. Comput. 12 (1983) 28-35.
36. A. Kolen, Location Problems on Trees and the Rectilinear Plane (Stichting Math. Centrum, Amsterdam, 1982).
37. O. Lefebvre, C. Michelot and F. Plastria, Geometric interpretation of the optimality conditions in multifacility location and applications, J. Optim. Theory Appl. 65 (1990) 85-101.
38. p distances using convex programming, Oper. Res. 23 (1975) 581-587.
39. J.S.B. Mitchell, An optimal algorithm for shortest rectilinear path among obstacles in the plane, Abstracts first Canadian Conference on Computational Geometry (1989).
40. H.M. Mulder, The Interval Function of a Graph, Mathematical Centre Tracts 132 (Mathematical Centre, Amsterdam, 1980).
41. L.M. Ostresh, The multifacility location problem: applications and descent theorems, J. Regional Sci. 17 (1977) 409-419.
42. J.C. Picard and H.D. Ratliff, A cut approach to the rectilinear distance facility location problem, Oper. Res. 26 (1978) 422-434.
43. F. Rado, The Euclidean multifacility location problem, Oper. Res. 36 (1988) 485-492.
44. G. Ruhe, Algorithmic Aspects of Flows in Networks (Kluwer, Dordrecht, 1991).
45. M. Sholander, Medians, lattices and trees, Proc. Amer. Math. Soc. 5 (1954) 808-812.
46. D.D. Sleator and R.E. Tarjan, A data structure for dynamic trees, J. Comput. System Sci. 24 (1983) 362-391.
47. P.S. Soltan and V. Chepoi, The solution of Weber problem for discrete median metric spaces, Trudy Tbiliss. Mat. Inst. 85 (1987) 52-76 (in Russian).
48. B.C. Tansel, R.L. Francis and T.J. Lowe, Location on networks: a survey I, II, Management Sci. 29 (1983) 482-511.
49. V.A. Trubin, An efficient algorithm for Weber problem with rectilinear metric, Kibernetika 6 (1978) 67-70 (in Russian).
50. M. van de Vel, Matching binary convexities, Topology Appl. 16 (1983) 207-235.
51. M. van de Vel, Theory of Convex Structures (Elsevier, Amsterdam, 1993).
52. E. Verheul, Multimedians in metric and normed spaces, Dissertation, Vrije Universiteit, Amsterdam (1991).
53. p-norm), European J. Oper. Res. 20 (1985) 373-381.
54. G.O. Wesolowski and R.F. Love, The optimal location of new facilities using rectilinear distances, Oper. Res. 19 (1971) 124-130.
55. D.K. Zambitski and V.K. Sibirski, An efficient algorithm for Weber problem on a tree network, Bull. Moldavian Acad. Sci. 2 (1980) 76-78 (in Russian).