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1 procedure BFS(G, root) is 2 let Q be a queue 3 label root as explored 4 Q.enqueue(root) 5 while Q is not empty do 6 v := Q.dequeue() 7 if v is the goal then 8 return v 9 for all edges from v to w in G.adjacentEdges(v) do 10 if w is not labeled as explored then 11 label w as explored 12 w.parent := v 13 Q.enqueue(w)
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 ...
The typical data structure in serial BFS and some parallel BFS is FIFO Queue, as it is simple and fast where insertion and delete operation costs only constant time. Another alternative is the bag-structure. [ 4 ]
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)} .
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 ...
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.
BFS will always find the path that has the fewest number of nodes which just happens to be the shortest path if all weights are the same. You certainly can modify BFS to use a priority queue instead of a normal queue so that it then really finds a shortest path. But then DFS is the same as BFS just with a stack instead of a queue.
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.