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Pangfeng Liu, Department of Computer Science and Information Engineering, National Taiwan University.
Graph Algorithms Pangfeng Liu, Department of Computer Science and - - PowerPoint PPT Presentation
Graph Algorithms Pangfeng Liu, Department of Computer Science and - - PowerPoint PPT Presentation
Graph Algorithms Pangfeng Liu, Department of Computer Science and Information Engineering, National Taiwan University. Articulation Points A node is an articulation point if its removal cause the connected component to break into more
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An Example
A B C D E F G H
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DFS Result
A B C D E F G H DFS Forward Edge B C D E A F H G
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Articulation Points
A node is an articulation point if there is no forward edge from its proper ancestor to the descendents of any of its children. This forward edge serves as a bypass from the upper part to the lower part, with the articulation point in the middle.
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The Number Low
Low is defined as the minimum of its traverse number and its descendent that has a back edge to its ancestor.
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The Low
1 2 3 4 5 6 7 8 1 1 1 3 3 3 3 8 BFS Back Edge B C D E A F H G A B C D E F G H 1 1 2 1
3 1 4 3 5 3 6 3 7 3 8 8
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The Low Computation
Initialize everyones low as its traverse number. The internal node simply takes the minimum with its children. If a forward edge is detected, modify the low of the descendent.
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Articulation Point Determination
If every child of a node v has a smaller low number than v, v is not an articulation point.
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