T. Radzik. Implementations of dynamic trees with in-subtree operations. ACM J. Experimental Algorithmics, 3:Article 9, 1998.  Home/Search   Document Details and Download   Summary   Related Articles

....believe part of the reason for their worse bounds and more complex solutions is diculties in working directly with Sleator and Tarjan s underlying representation. Of course, one may try to increase the applicability of the axiomatic interface by augmenting it with further operations. For example, [25] shows how to nd a minimum weight node in a subtree. However, dealing with non local properties is not so immediate, and we nd it unlikely that we will ever converge to a set of operations so big that we can forget about the underlying representation. The approach with top trees has instead ....

....ever converge to a set of operations so big that we can forget about the underlying representation. The approach with top trees has instead been concentrated on designing a representation which is very easy to deal with directly. For example, to compute the minimum node of a given subtree as in [25], since we can insert and delete edges, this is equivalent to maintaining the minimum node of each tree in a dynamic forest, and this is again done by maintaining, for each cluster, the minimum weight over its non boundary nodes. Since each node is only nonboundary in O(log n) clusters, weight ....

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T. Radzik. Implementations of dynamic trees with in-subtree operations. ACM J. Experimental Algorithmics, 3:Article 9, 1998.

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