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Minimizing diameters of dynamic trees

  • Session 5: Algorithms I
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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Abstract

In this paper we consider an on-line problem related to minimizing the diameter of a dynamic tree T. A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree TU {f}{e}. Starting with a tree with n nodes, we show how each such best swap can be found in worst-case O(log2 n) time. The problem was raised by Italiano and Ramaswami at ICALP'94 together with a related problem for edge deletions. Italiano and Ramaswami solved both problems in O(n) time per operation.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen, Denmark

    Stephen Alstrup, Jacob Holm, Kristian de Lichtenberg & Mikkel Thorup

Authors
  1. Stephen Alstrup
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  2. Jacob Holm
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  3. Kristian de Lichtenberg
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  4. Mikkel Thorup
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Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Alstrup, S., Holm, J., de Lichtenberg, K., Thorup, M. (1997). Minimizing diameters of dynamic trees. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_184

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  • DOI: https://doi.org/10.1007/3-540-63165-8_184

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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