Years and Authors of Summarized Original Work
2005; Tarjan, Werneck
Problem Definition
The dynamic tree problem is that of maintaining an arbitrary n-vertex forest that changes over time through edge insertions (links) and deletions (cuts). Depending on the application, one associates information with vertices, edges, or both. Queries and updates can deal with individual vertices or edges, but more commonly they refer to entire paths or trees. Typical operations include finding the minimum-cost edge along a path, determining the minimum-cost vertex in a tree, or adding a constant value to the cost of each edge on a path (or of each vertex of a tree). Each of these operations, as well as links and cuts, can be performed in \( { O(\log n) } \) time with appropriate data structures.
Key Results
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Recommended Reading
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Werneck, R.F. (2016). Dynamic Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_121
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