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The nearest common ancestor in a dynamic tree

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Summary

We consider the problem of determining the nearest common ancestor of two given nodes x and y (denoted by nca(x, y)) in a dynamic arbitrary tree T. We present an implementation of T by a pointer machine which needs linear space, performs m arbitrary insertions and deletions in the initially empty tree T in time O(m) and a query about nca(x, y) can be answered on-line in time O(log(min{depth(x), depth(y))+α(k,k))}, where the second factor is amortized over k queries, α is a functional inverse of Ackermann's function and depth(x) the distance from node x to the root of T.

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  1. Athanasios K. Tsakalidis

    Present address: Fachbereich 10, Informatik Universität des Saarlandes, D-6600, Saarbrücken, Federal Republic of Germany

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  1. Computer Technology Institute, P.O. Box 1122, Patras, Greece

    Athanasios K. Tsakalidis

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  1. Athanasios K. Tsakalidis
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Tsakalidis, A.K. The nearest common ancestor in a dynamic tree. Acta Informatica 25, 37–54 (1988). https://doi.org/10.1007/BF00268844

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  • DOI: https://doi.org/10.1007/BF00268844

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