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Single Facility Location: Circle Covering Problem

Sylvester's Problem

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Encyclopedia of Optimization
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References

  1. Blumenthal LM, Wahlin GE (1941) On the spherical surface of smallest radius enclosing a bounded subset of n‑dimensional Euclidean space. Amer Math Soc Bull 47:771–777

    Article  MathSciNet  MATH  Google Scholar 

  2. Boffey TB, Karkazis J (1983) Speeding up the Elzinga-Hearn algorithm for finding 1-centres. J Oper Res Soc 34:1119–1121

    Article  MATH  Google Scholar 

  3. Chakraborty RK, Chaudhuri PK (1981) A note on geometrical solutions for some minimax location problems. Trans Sci 15:164–166

    Article  MathSciNet  Google Scholar 

  4. Charalambous C (1981) An iterative algorithm for the minimax multifacility location problem with Euclidean distance. Naval Res Logist Quart 28:325–337

    Article  MathSciNet  MATH  Google Scholar 

  5. Chrystal G (1885) On the problem to construct the minimum circle enclosing n given points in the plane. Proc Edinburgh Math Soc 3:30–33

    Article  Google Scholar 

  6. Drezner Z, Shelah G (1987) On the complexity of the Elzinga–Hearn algorithm for the 1-center problem. Math Oper Res 12:255–261

    Article  MathSciNet  MATH  Google Scholar 

  7. Drezner Z, Wesolowsky GO (1983) Minimax and maximin facility location problems on a sphere. Naval Res Logist Quart 30:305–312

    Article  MathSciNet  MATH  Google Scholar 

  8. Elzinga J, Hearn DW (1972) Geometrical solutions for some minimax location problems. Trans Sci 6:379–394

    Article  MathSciNet  Google Scholar 

  9. Elzinga J, Hearn DW (1972) The minimum covering sphere problem. Managem Sci 19:96–104

    MathSciNet  MATH  Google Scholar 

  10. Elzinga J, Hearn DW (1974) The minimum sphere covering a convex polyhedron. Naval Res Logist Quart 21:715–718

    Article  MathSciNet  Google Scholar 

  11. Francis RL, McGinnis LF Jr, White JA (1992) Facility and location: An analytical approach, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  12. Hearn DW (1971) Minimum covering spheres. PhD Thesis Johns Hopkins Univ.,).

    Google Scholar 

  13. Hearn DW, Vijay J (1981) A geometrical solution for the weighted minimum circle problem. Res. Report ISE Dept. Univ. Florida 81(2)

    Google Scholar 

  14. Hearn DW, Vijay J (1982) Efficient algorithms for the (weighted) minimum circle problem. Oper Res 30:777–795

    Article  MathSciNet  MATH  Google Scholar 

  15. Hearn DW, Vijay J (1995) Codes of geometrical algorithms for the (weighted) minimum circle problem. Europ J Oper Res 80:236–237

    Article  Google Scholar 

  16. Jacobsen SK (1981) An algorithm for the minimax Weber problem. Europ J Oper Res 6:144–148

    Article  MathSciNet  MATH  Google Scholar 

  17. John F (1948) Extremum problems with inequalities as subsidiary conditions. Courant Anniv. Vol. Interscience 187–204

    Google Scholar 

  18. Konno H, Yajima Y, Ban A (1994) Calculating a minimal sphere containing a polytope defined by a system of linear inequalities. Comput Optim Appl 3:181–191

    Article  MathSciNet  MATH  Google Scholar 

  19. Kuhn HW (1975) Nonlinear programming: A historical view. SIAM-AMS Proc 9:1–26

    Google Scholar 

  20. Kuhn HW, Tucker AW (1950) Nonlinear programming. In: Neyman J (ed) Proc. Second Berkeley Symp. Math. Statistics and Probability. Univ. Calif. Press, Berkeley, CA, pp 481–492

    Google Scholar 

  21. Lawson CL (1965) The smallest covering cone or sphere. SIAM Rev 7:415–417

    Article  Google Scholar 

  22. Megiddo N (1983) Linear time algorithms for linear programming in R3 and related problems. SIAM J Comput 12:759–776

    Article  MathSciNet  MATH  Google Scholar 

  23. Nair KPK, Chandrasekaran R (1971) Optimal location of a single service center of certain types. Naval Res Logist Quart 18:503–510

    Article  MathSciNet  Google Scholar 

  24. Patel MH (1995) Spherical minimax location problem using the Euclidean norm: Formulation and optimization. Comput Optim Appl 4:79–90

    Article  MathSciNet  MATH  Google Scholar 

  25. Preparata FP, Shamos. MI (1985) Computational geometry: An introduction. Springer, Berlin

    Google Scholar 

  26. Rademacher H, Toeplitz O (1957) The enjoyment of mathematics. Princeton Univ. Press, Princeton. Transl. from: Von Zahlen and Figuren. Springer, 1933

    MATH  Google Scholar 

  27. Shamos MI, Hoey D (1975) Closest point problems. In: Proc. 16th IEEE Annual Symp., Found. of Comput. Sci., Berkeley, pp 151–162

    Google Scholar 

  28. Sylvester JJ (1857) A question in the geometry of situation. Quart J Pure Appl Math 1:79

    Google Scholar 

  29. Sylvester JJ (1860) On Poncelet's approximate linear valuation of surd froms. Philosophical Mag (Fourth Ser) 20:203–222

    Google Scholar 

  30. Welzl E (1991) Smallest enclosing disks (balls and ellipsoids). Lecture Notes Computer Sci, vol 555. Springer, Berlin, pp 359–370

    Google Scholar 

  31. Xue G, Sun S (1995) The spherical one-center problem. In: Du D-Z and Pardalos PM (eds) Minimax and Applications. Kluwer, Dordrecht, pp 153–156

    Google Scholar 

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Hearn, D.W. (2008). Single Facility Location: Circle Covering Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_620

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