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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 ...
Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
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 ...
The text alongside the figure says "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." However, the dark green nodes are not lowest common ancestors – they are not even ancestors but descendants. I hope I could make my point clearer now.
The LCP array is also an essential part of compressed suffix trees which provide full suffix tree functionality like suffix links and lowest common ancestor queries. [5] [6] Furthermore, it can be used together with the suffix array to compute the Lempel-Ziv LZ77 factorization in () time. [2] [7] [8] [9]
English: A directed acyclic graph with the common ancestors of two nodes in green, and their lowest common ancestors in dark green. Date 5 August 2014, 11:04:41