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Parametric search and locating supply centers in trees

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Book cover Algorithms and Data Structures (WADS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 519))

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Abstract

Linear-time and -space algorithms are presented for solving three versions of the p-center problem in a tree. The techniques are an application of parametric search.

This research was supported in part by the National Science Foundation under grants CCR-86202271 and CCR-9001241, and by the Office of Naval Research under contract N00014-86-K-0689.

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References

  1. P. K. Agarwal, B. Aronov, M. Sharir, and S. Suri. Selecting distances in the plane. April 1990.

    Google Scholar 

  2. E. M. Arkin and C. H. Papadimitriou. On the complexity of circulations. J. Algorithms, 7:134–145, 1986.

    Google Scholar 

  3. R. I. Becker, Y. Perl, and S. R. Schach. A shifting algorithm for min-max tree partitioning. J. ACM, 29:58–67, 1982.

    Google Scholar 

  4. R. Chandrasekaran and A. Tamir. Polynomially bounded algorithms for locating p-centers on a tree. Math. Prog., pages 304–315, 1982.

    Google Scholar 

  5. R. Cole. Partitioning point sets in arbitrary dimensions. Theor. Comput. Sci., 49:239–265, 1987.

    Google Scholar 

  6. R. Cole. Slowing down sorting networks to obtain faster sorting algorithms. J. ACM, 34:200–208, 1987.

    Google Scholar 

  7. R. Cole, J. S. Salowe, W. L. Steiger, and E. Szemeredi. An optimal-time algorithm for slope selection. SIAM J. Comput., 18:792–810, 1989.

    Google Scholar 

  8. R. Cole, M. Sharir, and C. K. Yap. On k-hulls and related problems. SIAM J. Comput., 17:61–77, 1987.

    Google Scholar 

  9. G. N. Frederickson. Optimal algorithms for partitioning trees and locating p-centers in trees. Technical report CSD-TR-1029, Purdue University, 1990.

    Google Scholar 

  10. G. N. Frederickson. Optimal algorithms for tree partitioning. In Proc. 2nd ACM-SIAM Symposium on Discrete Algorithms, pages 168–177, 1991.

    Google Scholar 

  11. G. N. Frederickson and D. B. Johnson. Finding kth paths and p-centers by generating and searching good data structures. J. Algorithms, 4:61–80, 1983.

    Google Scholar 

  12. G.N. Frederickson and D. B. Johnson. Generalized selection and ranking: sorted matrices. SIAM J. on Computing, 13:14–30, 1984.

    Google Scholar 

  13. A. J. Goldman. Optimal center location in simple networks. Transport. Sci., 5:212–233, 1971.

    Google Scholar 

  14. A. J. Goldman. Minimax location of a facility in an undirected tree graph. Transport. Sci., 6:407–418, 1972.

    Google Scholar 

  15. D. Gusfield. Parametric combinatorial computing and a problem of program module distribution. J.ACM, 30:551–563, 1983.

    Google Scholar 

  16. S. L. Hakimi. Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Res., 12:450–459, 1964.

    Google Scholar 

  17. G. Y. Handler. Minimax location of a facility in an undirected tree graph. Transport. Sci., 7:287–293, 1973.

    Google Scholar 

  18. G. Y. Handler. Finding two-centers of a tree: the continuous case. Transport. Sci., 12:93–106, 1978.

    Google Scholar 

  19. R. Hassin and A. Tamir. Efficient algorithms for optimization and selection on series-parallel graphs. SIAM J. Alg. Disc. Meth., 7:379–389, 1986.

    Google Scholar 

  20. D. H. Hochbaum and D. B. Schmoys. Approximation algorithms for bottleneck problems. J. ACM, 33:533–550, 1986.

    Google Scholar 

  21. O. Kariv and S. L. Hakimi. An algorithmic approach to network location problems. SIAM J. Appl. Math., 37:513–538, 1979.

    Google Scholar 

  22. C. Lo and W. Steiger. An optimal-time algorithm for ham-sandwich cuts in the plane. September 1990.

    Google Scholar 

  23. N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM, 30:852–865, 1983.

    Google Scholar 

  24. N. Megiddo and A. Tamir. New results on the complexity of p-center problems. SIAM J. Comput., 12:751–758, 1983.

    Google Scholar 

  25. N. Megiddo, A. Tamir, E. Zemel, and R. Chandrasekaran. An O(n log2 n) algorithm for the kth longest path in a tree with applications to location problems. SIAM J. Comput., 10:328–337, 1981.

    Google Scholar 

  26. Y. Perl and S. R. Schach. Max-min tree partitioning. J. ACM, 28:5–15, 1981.

    Google Scholar 

  27. R. Pollack and M. Sharir. Computing the geodesic center of a simple polygon. Technical Report 231, Courant Institute, September 1986.

    Google Scholar 

  28. M. Reichling. On the detection of a common intersection of k-convex polyhedra. Lect. Notes Comput. Sci., 333:180–187, 1988.

    Google Scholar 

  29. J. S. Salowe. L-infinity interdistance selection by parametric search. Inf. Proc. Lett., 30:9–14, 1989.

    Google Scholar 

  30. J. T. Schwartz and M. Sharir. Finding effective ‘force-targets’ for two-dimensional multifinger frictional grips. Technical Report 379, Courant Institute, June 1988.

    Google Scholar 

  31. E. Zemel. A linear time randomizing algorithm for searching ranking functions. Algorithmica, 2:81–90, 1987.

    Google Scholar 

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Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1991 Springer-Verlag Berlin Heidelberg

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Frederickson, G.N. (1991). Parametric search and locating supply centers in trees. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028271

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  • DOI: https://doi.org/10.1007/BFb0028271

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54343-5

  • Online ISBN: 978-3-540-47566-8

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