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Breadth-first search can be generalized to both undirected graphs and directed graphs with a given start node (sometimes referred to as a 'search key'). [4] In state space search in artificial intelligence , repeated searches of vertices are often allowed, while in theoretical analysis of algorithms based on breadth-first search, precautions ...
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.
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.
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 ...
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 ...
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.
A breadth-first search partitions the vertices of the graph into layers. The free vertices in U {\displaystyle U} are used as the starting vertices of this search and form the first layer of the partitioning.