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Breadth-first search ... An enumeration of the vertices of a graph is said to be a BFS ordering if it is the possible output of the application of BFS to this graph.
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.
A breadth-first search (BFS) is another technique for traversing a finite graph. BFS visits the sibling vertices before visiting the child vertices, and a queue is used in the search process. This algorithm is often used to find the shortest path from one vertex to another.
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 breadth-first search starts at , and the shortest distance () of each vertex from is recorded, dividing the graph into discrete layers. Additionally, each vertex v {\displaystyle v} keeps track of the set of vertices which in the preceding layer which point to it, p ( v ) {\displaystyle p(v)} .
Graph algorithms have long taken advantage of the idea that a graph can be represented as a matrix, and graph operations can be performed as linear transformations and other linear algebraic operations on sparse matrices. [6]: xxv–xxvi For example, matrix-vector multiplication can be used to perform a step in a breadth-first search.
Best-first search is a class of search algorithms which explores a graph by expanding the most promising node chosen according to a specified rule.. Judea Pearl described best-first search as estimating the promise of node n by a "heuristic evaluation function () which, in general, may depend on the description of n, the description of the goal, the information gathered by the search up to ...
In computer science, lexicographic breadth-first search or Lex-BFS is a linear time algorithm for ordering the vertices of a graph. The algorithm is different from a breadth-first search , but it produces an ordering that is consistent with breadth-first search.