Abstract
A bulk insertion for a given set of keys inserts all keys in the set into a leaf-oriented AVL-tree. Similarly, a bulk deletion deletes them all. The bulk insertion is simple if all keys fall in the same leaf position in the AVL-tree. We prove that simple bulk insertions and deletions of m keys have amortized complexity O(log m) for the tree adjustment phase. Our reasoning implies easy proofs for the amortized constant rebalancing cost of single insertions and deletions in AVL-trees. We prove that in general, the bulk operation composed of several simple ones of sizes m 1,..., m k has amortized complexity O(Σ ki=1 log m i).
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Soisalon-Soininen, E., Widmayer, P. (2002). Amortized Complexity of Bulk Updates in AVL-Trees. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_45
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DOI: https://doi.org/10.1007/3-540-45471-3_45
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