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If G is a tree, replacing the queue of this breadth-first search algorithm with a stack will yield a depth-first search algorithm. For general graphs, replacing the stack of the iterative depth-first search implementation with a queue would also produce a breadth-first search algorithm, although a somewhat nonstandard one. [10]
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 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.
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 wavefront expansion algorithm is a specialized potential field path planner with breadth-first search to avoid local minima. [1] [2] It uses a growing circle around the robot. The nearest neighbors are analyzed first and then the radius of the circle is extended to distant regions. [3]
The GraphBLAS specification has been in development since 2013, [15] and has reached version 2.1.0 as of December 2023. [16] While formally a specification for the C programming language, a variety of programming languages have been used to develop implementations in the spirit of GraphBLAS, including C++, [17] Java, [18] and Nvidia CUDA.
Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. [3] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch.
Partition refinement was applied by Sethi (1976) in an efficient implementation of the Coffman–Graham algorithm for parallel scheduling. Sethi showed that it could be used to construct a lexicographically ordered topological sort of a given directed acyclic graph in linear time; this lexicographic topological ordering is one of the key steps ...