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The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree
An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once
With the Euler tour technique, a tree could be represented in a flat style, and thus prefix sum could be applied to an arbitrary tree in this format. In fact, prefix sum can be used on any set of values and binary operation which form a group: the binary operation must be associative, every value must have an inverse, and there exists an ...
Print/export Download as PDF; Printable version; ... Euler tour technique; External memory graph traversal; Extremal Ensemble Learning; F. FKT algorithm;
Created Date: 8/30/2012 4:52:52 PM
[2] [4] This solution is based on the Euler tour technique for processing trees. The main observation is that LA(v,d) is the first node of depth d that appears in the Euler tour after the last appearance of v. Thus, by constructing the Euler tour and associated information on depth, the problem is reduced to a query on arrays, named find ...
Another data structure that can be used for the same purpose is Euler tour tree. In solving the maximum flow problem , link/cut trees can be used to improve the running time of Dinic's algorithm from O ( V 2 E ) {\displaystyle O(V^{2}E)} to O ( V E log V ) {\displaystyle O(VE\log V)} .
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