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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 ...
In computer science, Tarjan's off-line lowest common ancestors algorithm is an algorithm for computing lowest common ancestors for pairs of nodes in a tree, based on the union-find data structure. The lowest common ancestor of two nodes d and e in a rooted tree T is the node g that is an ancestor of both d and e and that has the greatest depth ...
RMQs can be used to solve the lowest common ancestor problem [1] [2] and are used as a tool for many tasks in exact and approximate string matching. The LCA query LCA S (v, w) of a rooted tree S = (V, E) and two nodes v, w ∈ V returns the deepest node u (which may be v or w) on paths from the root to both w and v. Gabow, Bentley, and Tarjan ...
Range minimum query reduced to the lowest common ancestor problem. Main article: Range minimum query When the function of interest in a range query is a semigroup operator, the notion of f − 1 {\displaystyle f^{-1}} is not always defined, so the strategy in the previous section does not work.
All of the following problems can be solved in O(Prefix sum(n)) (the time it takes to solve the prefix sum problem in parallel for a list of n items): Classifying advance and retreat edges: Do list ranking on the ETR and save the result in a two-dimensional array A. Then (u,v) is an advance edge iff A(u,v) < A(v,u), and a retreat edge otherwise.
If the tree is traversed from the bottom up with a bit vector telling which strings are seen below each node, the k-common substring problem can be solved in () time. If the suffix tree is prepared for constant time lowest common ancestor retrieval, it can be solved in Θ ( N ) {\displaystyle \Theta (N)} time.
The level ancestor query LA(v,d) requests the ancestor of node v at depth d, where the depth of a node v in a tree is the number of edges on the shortest path from the root of the tree to node v. It is possible to solve this problem in constant time per query, after a preprocessing algorithm that takes O( n ) and that builds a data structure ...
2. A rooted tree structure used to describe a cograph, in which each cograph vertex is a leaf of the tree, each internal node of the tree is labeled with 0 or 1, and two cograph vertices are adjacent if and only if their lowest common ancestor in the tree is labeled 1. cover A vertex cover is a set of vertices incident to every edge in a graph.