Path Minima Queries in Dynamic Weighted Trees
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چکیده
In the path minima problem on a tree, each edge is assigned a weight and a query asks for the edge with minimum weight on a path between two nodes. For the dynamic version of the problem, where the edge weights can be updated, we give data structures that achieve optimal query time in the comparison and the RAM models. These structures also support inserting a node on an edge, inserting a leaf, and contracting edges. When only insertion and deletion of leaves are desired, we give data structures in the comparison and the RAM models, with optimal query time that is significantly lower than when updating the weights is allowed. We also consider the problem in the semigroup model, and show lower bounds for different variants of the problem.
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تاریخ انتشار 2011