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If G is a tree, replacing the queue of the breadth-first search algorithm with a stack will yield a depth-first search algorithm. For general graphs, replacing the stack of the iterative depth-first search implementation with a queue would also produce a breadth-first search algorithm, although a somewhat nonstandard one. [7] Another possible ...
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
The problem of graph exploration can be seen as a variant of graph traversal. It is an online problem, meaning that the information about the graph is only revealed during the runtime of the algorithm. A common model is as follows: given a connected graph G = (V, E) with non-negative edge weights. The algorithm starts at some vertex, and knows ...
Trémaux trees are named after Charles Pierre Trémaux, a 19th-century French author who used a form of depth-first search as a strategy for solving mazes. [1] [2] They have also been called normal spanning trees, especially in the context of infinite graphs. [3] [4] All depth-first search trees and all Hamiltonian paths are Trémaux
An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
this gives you 1, 3, 4, 2 and not 1, 3, 2, 4, since 2 is labelled as discovered after 1 is popped, and hence it doesn't get pushed after 3 is popped. The underlying issue is that 2 occurs in two places in the graph, as a child of 1 and as a child of 3, and the place where it's discovered first is later in the depth-first order.
The basic idea of the algorithm is this: a depth-first search (DFS) begins from an arbitrary start node (and subsequent depth-first searches are conducted on any nodes that have not yet been found). As usual with depth-first search, the search visits every node of the graph exactly once, refusing to revisit any node that has already been visited.
A strong orientation of a given bridgeless undirected graph may be found in linear time by performing a depth-first search of the graph, orienting all edges in the depth-first search tree away from the tree root, and orienting all the remaining edges (which must necessarily connect an ancestor and a descendant in the depth-first search tree ...