You are running Kosaraju’s algorithm to find the SCCs of a directed graph. During the first DFS on the original directed graph 𝐺 , you record finishing times 𝑓 [ 𝑣 ] for all vertices. You then process vertices in decreasing order of finishing times when running the second DFS on the transpose graph . Which of the following statements accurately describe the behavior and meaning of these timings? 多项选择题
The vertex with the largest finishing time belongs to a “sink” SCC in the condensation graph
The second DFS, when started from the vertex with the largest finishing time, visits exactly one SCC and no others.
The second DFS must process vertices in decreasing order of finishing times in order to guarantee correctness of Kosaraju’s algorithm on all directed graphs.
Running the second DFS on G instead of GT would still correctly identify SCCs.
The vertex with the smallest finishing time belongs to a “source” SCC in the condensation graph .
If there is an edge from SCC C1 to SCC C2 in GSCC, then the maximum finishing time in C1 must be greater than the maximum finishing time in C2.
Kosaraju’s algorithm requires O(V2) time due to transposing the adjacency matrix.
The vertex with the largest finishing time in the first DFS always belongs to a source SCC in the condensation graph
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