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Titlebook: Algorithm Theory - SWAT ‘92; Third Scandinavian W Otto Nurmi,Esko Ukkonen Conference proceedings 1992 Springer-Verlag Berlin Heidelberg 199

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Efficient rebalancing of chromatic search trees,log.(N+1)]−2 rebalancing operations per deletion, where . is the maximum size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which a
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https://doi.org/10.1007/978-3-531-90903-5the distance between any two vertices in . is larger than that distance in . by no more than a factor of .. This note concerns the problem of finding the sparsest 2-spanner in a given graph, and presents an approximation algorithm for this problem with approximation ratio log(.).
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https://doi.org/10.57088/978-3-7329-8946-1d in . time on . processors, in the randomized parallel comparison tree model, where . is an inverse of Ackerman‘s function. I prove similar bounds for the related problem of putting . values into a min-max heap.
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