Lecture16-sccomponents

Consequence the strongly connected components can be

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than the highest post number in C’. § Consequence : The strongly connected components can be linearized by arranging them in decreasing order of their post numbers.

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Step 1 § Reverse the graph to produce GR § Necessary to do the reversal explicitly? § Run depth-first search on GR
Problem 3.4 (ii)

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Problem 3.4 (ii)
Problem 3.4 (ii)

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Step 2 § How do we continue once a vertex belonging to the sink component has been discovered? § Recall: The strongly connected components can be linearized by arranging them in decreasing order of their post numbers. § Run DFS on G, keeping track of connected components Process the vertices beginning and breaking

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3 Questions § Is it correct? § Relies on the correctness of the properties we identified earlier § How long does it take? § 2 DFS passes § O(||V|| + ||E||) – again! § Can we do better?
Assignment § Write your reviews! § HW #11: § Practice using the SCC-finding algorithm § Due Wednesday § Read 4.1-4.5 § Shortest Paths § Breadth First Search § Dijkstra’s Algorithm
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• Spring '08
• Jones,M
• Graph Theory, Depth-first search, Directed acyclic graph, connected component, Strongly connected component

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