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Faster non-linear parametric search with applications to optimization and dynamic geometry

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LATIN'98: Theoretical Informatics (LATIN 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1380))

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Abstract

A technique for accelerating certain applications of parametric search to non-linear problems is presented, together with its applications to optimization on weighted graphs and to two problems in dynamic geometry on points moving in straight-line trajectories: computing the minimum diameter over all time and finding the time at which the length of the maximum spanning tree is minimized.

Supported in part by the National Science Foundation under grant CCR-9520946.

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References

  1. Pankaj Agarwal and Jiri Matousek. Ray shooting and parametric search. SIAM J. Computing, 22:794–806, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  2. Pankaj K. Agarwal, Micha Sharir, and Sivan Toledo. Applications of parametric search to geometric optimization. Journal of Algorithms, 17:292–318, 1994.

    Article  MathSciNet  Google Scholar 

  3. M. Ajtai, J. Komlós, and E. Szemerédi. Sorting in clog n parallel steps. Combinatorial, pages 1–19, 1983.

    Google Scholar 

  4. Nancy M. Amato, Michael T. Goodrich, and Edgar A. Ramos. Parallel algorithms for higher-dimensional convex hulls. In Proceedings 35th IEEE Symp. on Foundations of Computer Science, pages 683–694, 1994.

    Google Scholar 

  5. Manuel Blum, Robert W. Floyd, Vaughan Pratt, Ronald L. Rivest, and Robert E. Tarjan. Time bounds for selection. Journal of Computer and System Sciences, 7(4):448–461, 1973.

    Article  MathSciNet  MATH  Google Scholar 

  6. Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, and Micha Sharir. Diameter, width, closest line pair, and parametric searching. Discrete Comput. Geom., 10:183–196, 1993.

    MathSciNet  MATH  Google Scholar 

  7. Richard Cole. Slowing down sorting networks to obtain faster sorting algorithms. J. Assoc. Comput. Mach., 34(1):200–208, 1987.

    MathSciNet  Google Scholar 

  8. Richard Cole. Parallel merge sort. SIAM J. Computing, 17(4):770–785, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  9. David Fernández-Baca and Giora Slutzki. Optimal parametric search on graphs of bounded tree-width. Journal of Algorithms, 22:212–240, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Gupta, Ravi Janardan, and Michiel Smid. Fast algorithms for collision and proximity problems involving moving geometric objects. Computational Geometry: Theory and Applications, 6:371–391, 1996.

    MathSciNet  MATH  Google Scholar 

  11. Joseph Ja'Ja'. An Introduction to Parallel Algorithms. Addison-Wesley, Reading, MA, 1992.

    Google Scholar 

  12. Naoki Katoh, Takeshi Tokuyama, and Kazuo Iwano. On minimum and maximum spanning trees of linearly moving sets of points. Discrete Comput. Geom., 13:161–176, 1995.

    MathSciNet  MATH  Google Scholar 

  13. Nimrod Megiddo. Combinatorial optimization with rational objective functions. Math. Oper. Res., 4:414–424, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  14. Nimrod Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. Assoc. Comput. Mach., 30(4):852–865, 1983.

    MATH  MathSciNet  Google Scholar 

  15. Russ Miller and Quentin F. Stout. Efficient parallel convex hull algorithms. IEEE Trans. Computers, C-37:1605–1618, 1988.

    Article  MathSciNet  Google Scholar 

  16. Clyde Monma, Michael Paterson, Subhash Suri, and Frances Yao. Computing Euclidean maximum spanning trees. Algorithmica, 5:407–419, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  17. Franco P. Preparata and Michael Ian Shamos. Computational Geometry: An Introduction. Springer-Verlag, 1985.

    Google Scholar 

  18. Jörg Schwerdt, Michiel Smid, and Stefan Schirra. Computing the minimum diameter for moving points: an exact implementation using parametric search. In 13th ACM Symposium on Computational Geometry, Nice, France, 1997.

    Google Scholar 

  19. Sivan Toledo. Maximizing non-linear concave functions in fixed dimension, pages 429–447. World Scientific, Singapore, 1993.

    Google Scholar 

  20. Sivan Toledo and Micha Sharir. Extremal polygon containment problems. Computational Geometry: Theory and Applications, 4:99–118, 1994.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Iowa State University, 50011, Ames, IA, USA

    David Fernández-Baca

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  1. David Fernández-Baca
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Editor information

Cláudio L. Lucchesi Arnaldo V. Moura

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© 1998 Springer-Verlag Berlin Heidelberg

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Fernández-Baca, D. (1998). Faster non-linear parametric search with applications to optimization and dynamic geometry. In: Lucchesi, C.L., Moura, A.V. (eds) LATIN'98: Theoretical Informatics. LATIN 1998. Lecture Notes in Computer Science, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054308

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  • DOI: https://doi.org/10.1007/BFb0054308

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64275-6

  • Online ISBN: 978-3-540-69715-2

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