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Input: A graph G and a starting vertex root of G. Output: Goal state.The parent links trace the shortest path back to root [9]. 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 ...
A depth-first search (DFS) is an algorithm for traversing a finite graph. DFS visits the child vertices before visiting the sibling vertices; that is, it traverses the depth of any particular path before exploring its breadth. A stack (often the program's call stack via recursion) is generally used when implementing the algorithm.
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.
If G is a tree, replacing the queue of the 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. [7]
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.
During computation in a distributed graph algorithms, passing information along these edges implies communication. [ 10 ] Partitioning the graph needs to be done carefully - there is a trade-off between low communication and even size partitioning [ 11 ] But partitioning a graph is a NP-hard problem, so it is not feasible to calculate them.
Scan the tree starting from u (using any tree scan algorithm, such as DFS). Scan the tree starting from v. Do the above two procedures in parallel, i.e., either using two parallel processes, or by interleaving their steps (make a step of first scan, then a step of the second scan, then a step of the first scan, etc.).
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.