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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 ...
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 … r].
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. 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.
In a Cartesian tree, this minimum value can be found at the lowest common ancestor of the leftmost and rightmost values in the subsequence. For instance, in the subsequence (12,10,20,15,18) of the example sequence, the minimum value of the subsequence (10) forms the lowest common ancestor of the leftmost and rightmost values (12 and 18).
Tarjan's off-line lowest common ancestors algorithm Tarjan's algorithm for finding bridges in an undirected graph [ 1 ] Tarjan's algorithm for finding simple circuits in a directed graph [ 2 ]
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 problem of testing whether a given graph is k vertices away and/or t edges away from a cograph is fixed-parameter tractable. [14] Deciding if a graph can be k -edge-deleted to a cograph can be solved in O * (2.415 k ) time, [ 15 ] and k -edge-edited to a cograph in O * (4.612 k ). [ 16 ]