Nothing Special   »   [go: up one dir, main page]

Skip to main content

Maintaining Center and Median in Dynamic Trees

  • Conference paper
  • First Online:
Algorithm Theory - SWAT 2000 (SWAT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

Included in the following conference series:

Abstract

We show how to maintain centers and medians for a collection of dynamic trees where edges may be inserted and deleted and node and edge weights may be changed. All updates are supported in O(log n) time, where n is the size of the tree(s) involved in the update.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Kanevsky, R Tamassia, G. Battista, and J. Chen. On-line maintenance of the four-connected components of a graph (extended abstract). In 32nd FOCS, pages 793–801, 1991.

    Google Scholar 

  2. S. Alstrup, J. Holm, K de Lichtenberg, and M. Thorup. Minimizing diameters of dynamic trees. In ICALP’97, pages 270–280, 1997.

    Google Scholar 

  3. V. Auletta, D. Parente, and G. Persiano. Dynamic and static algorithms for optimal placement of resources in a tree. TCS, 165:441–461, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Battista and R. Tamassia. Incremental planarity testing (extended abstract). In 30th FOCS, pages 436–441, 1989.

    Google Scholar 

  5. G. Battista and R. Tamassia. On-line graph algorithms with SPQR-trees. In ICALP’90, pages 598–611, 1990.

    Google Scholar 

  6. S. Cheng and M. Ng. Isomorphism testing and display of symmetries in dynamic trees. In Proc. 7th SODA, 1996.

    Google Scholar 

  7. R. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13(3):245–265, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Cohen and R. Tamassia. Combine and conquer. Algorithmica, 18(3):324–362, 1997.

    Article  MathSciNet  Google Scholar 

  9. R. F. Cohen and R. Tamassia. Dynamic expression trees and their applications. In 2nd SODA, pages 52–61, 1991.

    Google Scholar 

  10. G. Frederickson. Data structures for on-line updating of minimum spanning trees, with applications. SICOMP, 14(4):781–798, 1985.

    MATH  MathSciNet  Google Scholar 

  11. G. Frederickson. Parametric search and locating supply centers in trees. In WADS’91, volume 519 of LNCS, pages 299–319, 1991.

    Google Scholar 

  12. G. Frederickson. Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. SICOMP, 26(2):484–538, 1997. See also FOCS’91.

    MATH  MathSciNet  Google Scholar 

  13. M. Fredman and M. Saks. The cell probe complexity of dynamic data structures. In Proc. 21st STOC, pages 345–354, 1989.

    Google Scholar 

  14. Z. Galil and G. Italiano. Maintaining biconnected components of dynamic planar graphs. In ICALP’91, 1991.

    Google Scholar 

  15. B. Gavish and S. Sridhar. Computing the 2-median on tree networks in O(n log n) time. Networks, 26, 1995. See also Networks Vol. 27, 1996.

    Google Scholar 

  16. A. Goldberg, M. Grigoriadis, and R. Tarjan. Use of dynamic trees in a network simplex algorithm for the maximum flow problem. Math. Programming, 50:277–290, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Goldman. Optimal center location in simple networks. Transportation Sci., 5:212–221, 1971.

    MathSciNet  Google Scholar 

  18. S. Hakimi and O. Kariv. An algorithmic approach to network location problems, ii: the p-medians. SIAM J. APPL. MATH., 37(3):539–560, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Handler. Minimax location of a facility in an undirected tree network. Transportation. Sci., 7:287–293, 1973.

    Article  MathSciNet  Google Scholar 

  20. M. R. Henzinger and V. King. Randomized dynamic graph algorithms with polylogarithmic time per operation. In Proc. 27th Symp. on Theory of Computing, pages 519–527, 1995.

    Google Scholar 

  21. J. A. La Poutré. Dynamic graph algorithms and data structures. PhD thesis, Dep. Comp. Sci., Utrecht Uni., 1991.

    Google Scholar 

  22. S. Peckham. Maintaining tree projections in amortized O(log n) time. Technical Report TR89-1034, Cornell Uni., Comp. Sci. Dep., 1989.

    Google Scholar 

  23. J. A. L. Poutré. Alpha-algorithms for incremental planarity testing. In 26th STOC, pages 706–715, 1994.

    Google Scholar 

  24. J. L. Poutré. Maintenance of triconnected components of graphs. In ICALP’92, volume 623 of LNCS, pages 354–365, 1992.

    Google Scholar 

  25. T. Radzik. Implementations of dynamic trees with in-subtree operations. ACM J. Experimental Algorithmics, 3:Article 9, 1998.

    Google Scholar 

  26. A. Rosenthal and J. Pino. A generalized algorithm for centrality problems on trees. J. ACM, 36:349–361, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  27. D. Sleator and R. Tarjan. A data structure for dynamic trees. JCSS, 26(3):362–391, 1983. See also STOC’81.

    MATH  MathSciNet  Google Scholar 

  28. R. Tarjan. A class of algorithms which require nonlinear time to maintain disjoint sets. Journal of computer and system sciences, 18(2):110–127, 1979. See also STOC 1977.

    Article  MATH  MathSciNet  Google Scholar 

  29. R. Tarjan. Dynamic trees and search trees via euler tours, applied to the network simplex algorithm. Technical Report 503–95, Dep. Comp. Sci., Princeton Uni., September 1995.

    Google Scholar 

  30. J. Westbrook and R. Tarjan. Maintaining bridge-connected and biconnected components on-line. Algorithmica, 7:433–464, 1992.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alstrup, S., Holm, J., Thorup, M. (2000). Maintaining Center and Median in Dynamic Trees. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-44985-X_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics