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 connected components. � It is like � weak point � within a network.

An Example D E C A F G B H

A DFS Result DFS B D Forward Edge E C C A D E F G B F H G H

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.

The Number � Low � � Low is defined as the minimum of its traverse number and its descendent that has a back edge to its ancestor.

The � Low � A 1 1 2 1 BFS B D 4 Back Edge 3 E 3 3 1 C 5 C 1 A 1 3 1 4 3 D 3 3 6 E 5 3 7 G F 2 1 8 6 3 B F 8 H G H 7 3 8 8

The � Low � Computation � Initialize everyone � s � 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.

Articulation Point Determination � If every child of a node v has a smaller low number than v, v is not an articulation point.

Articulation Point Determination BFS 4 3 Back Edge 3 5 1 1 3 1 3 3 6 7 2 1 8 8