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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 combinatorial mathematics and theoretical computer science, heavy-light decomposition (also called heavy path decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition, each non-leaf node selects one "heavy edge", the edge to the child that has the greatest number of descendants (breaking ...
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 ...
n November 1954, 29-year-old Sammy Davis Jr. was driving to Hollywood when a car crash left his eye mangled beyond repair. Doubting his potential as a one-eyed entertainer, the burgeoning performer sought a solution at the same venerable institution where other misfortunate starlets had gone to fill their vacant sockets: Mager & Gougelman, a family-owned business in New York City that has ...
Euler's proof of the degree sum formula uses the technique of double counting: he counts the number of incident pairs (,) where is an edge and vertex is one of its endpoints, in two different ways. Vertex v {\displaystyle v} belongs to deg ( v ) {\displaystyle \deg(v)} pairs, where deg ( v ) {\displaystyle \deg(v)} (the degree of v ...
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