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Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level.
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.
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 following pseudo-code of a 1-D distributed memory BFS [5] was originally designed for IBM BlueGene/L systems, which have a 3D torus network architecture. Because the synchronization is the main extra cost for parallelized BFS, the authors of this paper also developed a scalable all-to-all communication based on point-to-point communications .
Even and Itai also contributed to this algorithm by combining BFS and DFS, which is how the algorithm is now commonly presented. [ 2 ] For about 10 years of time after the Ford–Fulkerson algorithm was invented, it was unknown if it could be made to terminate in polynomial time in the general case of irrational edge capacities.
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Beam search uses breadth-first search to build its search tree. At each level of the tree, it generates all successors of the states at the current level, sorting them in increasing order of heuristic cost. [2] However, it only stores a predetermined number, , of best states at each level (called the beam width). Only those states are expanded ...
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.