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An arborescence of graph G is a directed tree of G which contains a directed path from a specified node L to each node of a subset V′ of V \{L}. Node L is called the root of arborescence. An arborescence is a spanning arborescence if V′ = V \{L}. MBST in this case is a spanning arborescence with the minimum bottleneck edge.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
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, the minimum routing cost spanning tree of a weighted graph is a spanning tree minimizing the sum of pairwise distances between vertices in the tree. It is also called the optimum distance spanning tree, shortest total path length spanning tree, minimum total distance spanning tree, or minimum average distance spanning tree.
The general graph Steiner tree problem can be approximated by computing the minimum spanning tree of the subgraph of the metric closure of the graph induced by the terminal vertices, as first published in 1981 by Kou et al. [18] The metric closure of a graph G is the complete graph in which each edge is weighted by the shortest path distance ...
The numbers beside the vertices indicate the distance from the root vertex. In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G.
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.