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Overview. In this lecture, we compare breath- rst search (BFS) and depth- rst search (DFS), two ways to traverse a graph, and study their applications. 11.1 Applications of Depth-First Search. cture, we detailed the DFS algorithm and introduced the notion of pre-order and post-order. To present our rst application of DFS, we .
•depth-first search(DFS): Finds a path between two vertices by exploring each possible path as far as possible before backtracking. –Often implemented recursively.
Graph traversal. Consider a graph, directed or undirected. The most basic graph problem is traversing the graph. There are two simple ways of traversing all vertices/edges in a graph in a systematic way: BFS and DFS. Basic idea: over the course of the traversal a vertex progresses from undiscovered, to discovered, to completely-discovered:
1 Depth First Search (DFS) We start graph algorithms with the pretty intuitive, but surprisingly powerful, depth first search (DFS). This algorithm solves the reachabilty problem, but then in one swoop solves much more. It also runs in ( n+ m) time. Let’s get to it. 1.1 DFS from a vertex
Graph Traversal Techniques: BFS and DFS. MTL 776 Graph Algorithms. Graph Representation. Two popular computer representations of a graph. Both represent the vertex set and the edge set, but in different ways. Adjacency Matrix. Use a 2D matrix to represent the graph. Adjacency List. Use a 1D array of linked lists. Adjacency Matrix.
DFS-based reachability. It turns out to be relatively straightforward to implement DFS by using nothing more than recursion. For simplicity, let’s consider a version of DFS that simply returns a set of reachable vertices, as we did with BFS.
Depth-first search (DFS) is an algorithm that allows us to systematically explore every vertex of a directed graph. The strategy used by DFS is the following: start at any vertex s and explore one path leading away from s until nothing new can be discovered.
