Reference Work Entry

Encyclopedia of Algorithms

pp 1-99

Dynamic Trees

2005; Tarjan, Werneck
  • Renato F. WerneckAffiliated withMicrosoft Research Silicon Valley

Keywords and Synonyms

Link-cut trees

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

Figure 1

An ST-tree (adapted from [14]). On the left, the original tree, rooted at a and already partitioned into paths; on the right, the actu ...

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