A simple linear algorithm for computing rectilinear 3-centers

Computational Geometry: Theory and Applications

Volumn 31, Issue 3, 2005, Pages 150-165

  Hoffmann, Michael ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Facility location; Geometric optimization; Rectilinear center

Indexed keywords

EID: 84867966435     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2004.12.002     Document Type: Article

References (30)

1. P.K. Agarwal, and C.M. Procopiuc Exact and approximation algorithms for clustering Algorithmica 33 2002 201 226
2. P.K. Agarwal, M. Sharir, and E. Welzl The discrete 2-center problem Discrete Comput. Geom. 20 1998 287 305
3. E. Assa, and M.J. Katz 3-piercing of d-dimensional boxes and homothetic triangles Internat. J. Comput. Geom. Appl. 8 1999 249 260
4. S.N. Bespamyathnikh, and M. Segal Rectilinear static and dynamic discrete 2-center problems Proc. 6th Workshop Algorithms Data Struct. Lecture Notes Comput. Sci. vol. 1663 1999 Springer Berlin 276 287
5. M. Blum, R.W. Floyd, V. Pratt, R.L. Rivest, and R.E. Tarjan Time bounds for selection J. Comput. Syst. Sci. 7 1973 448 461
6. CGAL. The Computational Geometry Algorithms Library http://www.cgal.org/
7. T.M. Chan More planar two-center algorithms Computational Geometry 13 1999 189 198
8. Z. Drezner On the rectangular p-center problem Naval Res. Logist. Q. 34 1987 229 234
9. M.E. Dyer On a multidimensional search technique and its application to the Euclidean one-centre problem SIAM J. Comput. 15 1986 725 738
10. D. Eppstein Faster construction of planar two-centers Proc. 8th ACM-SIAM Sympos. Discrete Algorithms 1997
11. T. Feder, and D.H. Greene Optimal algorithms for approximate clustering Proc. 20th Annu. ACM Sympos. Theory Comput. 1988 434 444
12. G.N. Frederickson, and D.B. Johnson Finding kth paths and p-centers by generating and searching good data structures J. Algorithms 4 1983 61 80
13. G.N. Frederickson, and D.B. Johnson Generalized selection and ranking: sorted matrices SIAM J. Comput. 13 1984 14 30
14. D. Halperin, M. Sharir, and K. Goldberg The 2-center problem with obstacles J. Algorithms 42 1 2002 109 134
15. M. Hoffmann Covering polygons with few rectangles Abstracts 17th European Workshop Comput. Geom. 2001 Freie Universität Berlin 39 42
16. J.W. Jaromczyk, and M. Kowaluk An efficient algorithm for the Euclidean two-center problem Proc. 10th Annu. ACM Sympos. Comput. Geom. 1994 303 311
17. M.J. Katz, K. Kedem, and M. Segal Discrete rectilinear 2-center problems Computational Geometry 15 2000 203 214
18. S. Khuller, and Y.J. Sussmann The capacitated k-center problem SIAM J. Discrete Math. 13 3 2000 403 418
19. L-distance Discrete Appl. Math. 40 1992 397 410
20. M.T. Ko, and R.C.T. Lee On weighted rectilinear 2-center and 3-center problems Inform. Sci. 54 1991 169 190
21. M.T. Ko, R.C.T. Lee, and J.S. Chang An optimal approximation algorithm for the rectilinear m-center problem Algorithmica 5 1990 341 352
22. J. Matoušek, M. Sharir, and E. Welzl A subexponential bound for linear programming Algorithmica 16 1996 498 516
23. N. Megiddo The weighted Euclidean 1-center problem Math. Oper. Res. 8 4 1983 498 504
24. N. Megiddo Linear programming in linear time when the dimension is fixed J. ACM 31 1984 114 127
25. N. Megiddo, and K.J. Supowit On the complexity of some common geometric location problems SIAM J. Comput. 13 1 1984 182 196
26. N. Megiddo, and E. Zemel A randomized O (nlogn) algorithm for the weighted Euclidean 1-center problem J. Algorithms 7 1986 358 368
27. D. Nussbaum Rectilinear p-piercing problems Proc. Annu. Internat. Sympos. Symbolic Algebraic Comput. 1997 316 323
28. M. Segal On piercing of axis-parallel rectangles and rings Proc. 5th Annu. European Sympos. Algorithms Lecture Notes Comput. Sci. vol. 1284 1997 Springer Berlin 430 442
29. M. Sharir A near-linear algorithm for the planar 2-center problem Discrete Comput. Geom. 18 1997 125 134
30. M. Sharir, and E. Welzl Rectilinear and polygonal p-piercing and p-center problems Proc. 12th Annu. ACM Sympos. Comput. Geom. 1996 122 132