Abstract
Given a rooted tree with n nodes, the tree shortcut problem is to add a set of shortcut edges to the tree such that the shortest path from each node to any of its ancestors is of length \(O(\log n)\) and the degree increment of each node is constant. We consider in this paper the dynamic version of the problem, which supports node insertion and deletion. For insertion, a node can be inserted as a leaf node or an internal node by sub-dividing an existing edge. For deletion, a leaf node can be deleted, or an internal node can be merged with its single child. We propose an algorithm that maintains a set of shortcut edges in \(O(\log n)\) time for an insertion or deletion.
This research is partially funded by a grant from Hong Kong RGC under the contract HKU17200214E.
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Chan, TH.H., Wu, X., Zhang, C., Zhao, Z. (2015). Dynamic Tree Shortcut with Constant Degree. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_34
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DOI: https://doi.org/10.1007/978-3-319-21398-9_34
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