Euler Tour Technique

The Euler tour technique is a method in graph theory and parallel computing for representing a tree so that many tree problems can be solved efficiently. It works by converting an undirected tree into a directed graph with each edge replaced by a pair of directed edges, which can then be traced out as a single Eulerian circuit, a closed walk that uses every edge exactly once. Introduced by Tarjan and Vishkin in 1984 and named for the technique's roots in Leonhard Euler's work on such circuits, the method allows classifying edges, computing the level and subtree size of each node, and finding depth-first search indices and lowest common ancestors, all with efficient parallel algorithms. When the Euler tour is combined with a balanced binary search tree, forming what is called an Euler tour tree, updates and queries on a changing forest of trees can be performed in logarithmic time. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/