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Path minima queries in dynamic weighted trees. (English) Zbl 1342.68106
Dehne, Frank (ed.) et al., Algorithms and data structures. 12th international symposium, WADS 2011, New York, NY, USA, August 15–17, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-22299-3/pbk). Lecture Notes in Computer Science 6844, 290-301 (2011).
Summary: In the path minima problem on trees each tree 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 on a tree, where the edge-weights can be updated, we give comparison-based and RAM data structures that achieve optimal query time. These structures support inserting a node on an edge, inserting a leaf, and contracting edges. When only insertion and deletion of leaves in a tree are needed, we give two data structures that achieve optimal and significantly lower query times than when updating the edge-weights is allowed. One is a semigroup structure for which the edge-weights are from an arbitrary semigroup and queries ask for the semigroup-sum of the edge-weights on a given path. For the other structure the edge-weights are given in the word RAM. We complement these upper bounds with lower bounds for different variants of the problem.
For the entire collection see [Zbl 1219.68015].

68P05 Data structures
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