- 1.T. Y. Chan. More planar two-center algorithms. Comput. Geom. Theory Appl., 13:189-198, 1999. Google ScholarDigital Library
- 2.S.-W. Cheng, O. Cheong, H. Everett, and R. van Oostrum. Hierarchical vertical decomposition, ray shooting, and circular arc queries in simple polygons. In Proc. 15th Annu. A CM Sympos. Comput. Geom., pages 227-236, 1999. Google ScholarDigital Library
- 3.R. Cole. Slowing down sorting networks to obtain faster sorting algorithms. ?. A CM, 34(1):200-208, 1987. Google ScholarDigital Library
- 4.R. Cole, J. Salowe, W. Steiger, and E. Szemerddi. An optimal-time algorithm for slope selection. SIAM J. Cornput., 18(4):792-810, 1989. Google ScholarDigital Library
- 5.J. Craig. Geometric algorithms in Adept RAPID. In P. K. Agarwal, L. Kavraki, and M. Mason, editors, Third Workshop on Algorithmic Foundations oJ Robotics, pages 133- 139. A. K. Peters, Ltd, Wellesley, MA, 1998. Google ScholarDigital Library
- 6.D. Eppstein. Dynamic three-dimensional linear programming. In Proc. 3~nd Annu. IEEE Sympos. Found. Comput. Sci., pages 488-494, 1991. Google ScholarDigital Library
- 7.D. Eppstein. Faster construction of planar two-centers. In Proc. 8th A CM-SIAM Sympos. Discrete Algorithms, pages 131-138, 1997. Google ScholarDigital Library
- 8.D. Halperin and C. Linhart. The minimum enclosing disk with obstacles. Manuscript, 1999. Java applet: http://www, m a t h .tau .ac.il/,~ ha I perin / projects, html.Google Scholar
- 9.P. Hansen, B. Jaumard, and H. Tuy. Global optimization in location. In Z. Drezner, editor, Facility Location, pages 43-68. Springer-Verlag, New York, 1995.Google ScholarCross Ref
- 10.K. Kedem, R. Livne, J. Pach, and M. Sharir. On the union of Jordan regions and collision-free translation al motion amidst polygonal obstacles. Discrete Uomput. Geom., 1:59- 71, 1986. Google ScholarDigital Library
- 11.J. Matouiek, N. Miller, J. Pach, M. Sharir, S. Sifrony, and E. Welzl. Fat triangles determine linearly many holes. In Proc. 3~nd Annu. IEEE Sympos. Found. Comput. Sci., pages 49-58, 1991. Google ScholarDigital Library
- 12.N. Megiddo. Linear-time algorithms for linear programming in Rs and related problems. SIAM Y. Comput., 12:759-776, 1983.Google ScholarCross Ref
- 13.N. Megiddo and K. J. Supowit. On the complexity of some common geometric location problems. SIAM J. Comput., 13(1):182-196, 1984.Google ScholarCross Ref
- 14.M. H. Overmars and J. van Leeuwen. Maintenance of configurations in the plane. Y. Comput. Syst. Sci., 23:166-204, 1981.Google ScholarCross Ref
- 15.M. Sharir. A near-linear algorithm for the planar 2-center problem. Discrete Comput. Geom., 18:125-134, 1997.Google ScholarCross Ref
Index Terms
- The 2-center problem with obstacles
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