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Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
In this context, a search method is described as being complete if it is guaranteed to find a goal state if one exists. Breadth-first search is complete, but depth-first search is not. When applied to infinite graphs represented implicitly, breadth-first search will eventually find the goal state, but depth first search may get lost in parts of ...
The breadth-first-search algorithm is a way to explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms. For instance, BFS is used by Dinic's algorithm to find maximum flow in a graph.
By contrast, a breadth-first search will never reach the grandchildren, as it seeks to exhaust the children first. A more sophisticated analysis of running time can be given via infinite ordinal numbers ; for example, the breadth-first search of the depth 2 tree above will take ω ·2 steps: ω for the first level, and then another ω for the ...
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 ...
This tree is known as a depth-first search tree or a breadth-first search tree according to the graph exploration algorithm used to construct it. [18] Depth-first search trees are a special case of a class of spanning trees called Trémaux trees, named after the 19th-century discoverer of depth-first search. [19]
The algorithm is called lexicographic breadth-first search because the order it produces is an ordering that could also have been produced by a breadth-first search, and because if the ordering is used to index the rows and columns of an adjacency matrix of a graph then the algorithm sorts the rows and columns into lexicographical order.
Breadth-first search can be viewed as a special-case of Dijkstra's algorithm on unweighted graphs, where the priority queue degenerates into a FIFO queue. The fast marching method can be viewed as a continuous version of Dijkstra's algorithm which computes the geodesic distance on a triangle mesh.