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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
[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 ...
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
In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [2]
A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph . Similar notions may be defined for directed graphs , where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices ...
This article describes techniques; for a history of the movement of tectonic plates, see Geological history of Earth.. Plate reconstruction is the process of reconstructing the positions of tectonic plates relative to each other (relative motion) or to other reference frames, such as the Earth's magnetic field or groups of hotspots, in the geological past.
This page was last edited on 10 April 2004, at 14:21 (UTC).; Text is available under the