Undirected versus Directed Graphs

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Presentation transcript:

Undirected versus Directed Graphs BBM 204 Algorithms Lab Recitation7 Undirected versus Directed Graphs Directed Graphs Strongly Components Işıl Karabey

Index Undirected versus Directed Graphs Directed Graphs DFS and BFS in Directed Graphs Strongly Components Exercises for directed graphs

Undirected versus Directed Graphs Source: http://www.inf.ed.ac.uk/teaching/courses/cs2/LectureNotes/CS2Bh/ADS/lecture9.pdf

Representation of Undirected and Directed Graphs Source: https://courses.cs.washington.edu/courses/cse326/00wi/handouts/lecture21/sld014.htm

Example of Graphs in Real Life Source: http://www.inf.ed.ac.uk/teaching/courses/cs2/LectureNotes/CS2Bh/ADS/lecture9.pdf

Examples Cont’d Source: http://www.inf.ed.ac.uk/teaching/courses/cs2/LectureNotes/CS2Bh/ADS/lecture9.pdf

Examples Cont’d Source: http://www.inf.ed.ac.uk/teaching/courses/cs2/LectureNotes/CS2Bh/ADS/lecture9.pdf

Directed Graphs A directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them Source: https://en.wikipedia.org/wiki/Directed_graph

Digraph Representation Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf

Drawing a Digraph Source: Source: Algorithms, 4th Edition, R. Sedgewick and K. Wayne, Addison-Wesley Professional, 2011 (Chapter 4, Exercises 4.1.2, pp. 696)

Recall Source: Algorithms, 4th Edition, R. Sedgewick and K. Wayne, Addison-Wesley Professional, 2011 (Chapter 4, pp. 525

Recall Adjacency-list digraph representation Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf

Graph Traversals Source: http://www.inf.ed.ac.uk/teaching/courses/cs2/LectureNotes/CS2Bh/ADS/lecture9.pdf

Depth-first search in digraphs Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf

Depth-first search (single-source reachability)

Depth-first search (DFS) Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf

Breadth-first search in digraphs Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf

Digraph BFS application: Web Crawler Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf

Breadth-first search (single-source reachability)

Strongly Connected Directed graphs Every pair of vertices are reachable from each other Source: www.cs.bu.edu/~steng/teaching/Fall2003/.../lecture16.ppt

Strongly Connected Source: www.cs.bu.edu/~steng/teaching/Fall2003/.../lecture16.ppt

Strongly Connected Components Source: www.cs.bu.edu/~steng/teaching/Fall2003/.../lecture16.ppt

Kosaraju's algorithm for Strongly Components call DFS(G) to compute finishing times f[u] for each vertex u. compute GT call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing f[u] output the vertices of each tree in the depth-first forest of step 3 as a separate strongly connected component. The graph GT is the transpose of G, which is visualized by reversing the arrows on the digraph. Source: www.cs.bu.edu/~steng/teaching/Fall2003/.../lecture16.ppt

Digraph-processing summary Source: https://www.cs.princeton.edu/~rs/AlgsDS07/13DirectedGraphs.pdf