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A linear-time algorithm for finding a longest path in a tree was proposed by Edsger Dijkstra around 1960, while a formal proof of this algorithm was published in 2002. [15] Furthermore, a longest path can be computed in polynomial time on weighted trees, on block graphs, on cacti, [16] on bipartite permutation graphs, [17] and on Ptolemaic ...
For example, in a chess endgame, a chess engine may build the game tree from the current position by applying all possible moves and use breadth-first search to find a win position for White. Implicit trees (such as game trees or other problem-solving trees) may be of infinite size; breadth-first search is guaranteed to find a solution node [1 ...
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 ...
Dijkstra's algorithm finds the shortest path from a given source node to every other node. [7]: 196–206 It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of ...
Storing the paths through the tree in a skew binary random access list allows the tree to still be extended downward one O(1) step at a time, but now allows the search to proceed in O(log(p)), where "p" is the distance from v to the requested depth. This approach is feasible when the tree is particularly wide or will be extended online and so ...
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
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 ...
Edmonds' algorithm (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings; Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane; Longest path problem: find a simple path of maximum length in a given graph; Minimum spanning tree. Borůvka's algorithm ...