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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© 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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