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An optimal approximation algorithm for the rectilinearm-center problem

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Abstract

Given a set ofn points on the plane, the rectilinearm-center problem is to findn rectilinear squares covering all thesen points such that the maximum side length of these squares is minimized. In this paper we prove that there is no polynomial-time algorithm with an error ratio ɛ < 2 for the rectilinearm-center problem unless NP = P. A polynomial-time approximation algorithm with an error ratio of 2 is also proposed.

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References

  • Drezner, Z., On the rectangularp-center problem,Naval Research Logistics, vol. 34, no. 2, 1987, pp. 229–234.

    Article  MATH  MathSciNet  Google Scholar 

  • Drezner, Z., and Wesolowsky, G. O., Single facilityl p -distance minimax location,SIAM Journal on Algebraic and Discrete Methods, vol. 1, no. 3, September 1980, pp. 315–321.

    Article  MATH  MathSciNet  Google Scholar 

  • Elzinga, J., and Hearn, D. W., Geometrical solution for some minimax location problems,Transportation Science, vol. 6, no. 4, 1972, pp. 379–394.

    Article  MathSciNet  Google Scholar 

  • Garey, M. R., and Johnson, D. S.,Computers and Intractability: A Guide to the Theory of NP Completeness, W. H. Freeman & Co., San Francisco, 1979.

    MATH  Google Scholar 

  • Hochbaum, D. S., and Shmoys, D. B., A unified approach to approximation algorithms for bottleneck problems,Journal of the Association for Computing Machinery, vol. 33, no. 3, July 1986, pp. 533–550.

    MathSciNet  Google Scholar 

  • Megiddo, N., and Supowit, K. J., On the complexity of some common geometric location problems,SIAM Journal on Computing, vol. 13, no. 1, February 1984, pp. 182–196.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Computer and Decision Sciences, National Tsing Hua University, Hsinchu, Taiwan, Republic of China

    M. T. Ko & J. S. Chang

  2. National Tsing Hua University, Hsinchu, Taiwan

    R. C. T. Lee

  3. The Academia Sinica, Taipei, Taiwan, Republic of China

    R. C. T. Lee

Authors
  1. M. T. Ko
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  2. R. C. T. Lee
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  3. J. S. Chang
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Additional information

Communicated by D. T. Lee.

This research work was partially supported by a grant from the National Science Council of the Republic of China under Grant NSC-77-0408-E007-03.

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Ko, M.T., Lee, R.C.T. & Chang, J.S. An optimal approximation algorithm for the rectilinearm-center problem. Algorithmica 5, 341–352 (1990). https://doi.org/10.1007/BF01840393

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  • DOI: https://doi.org/10.1007/BF01840393

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