Biconnectivity-new-handouts-2 - Biconnectivity 1:49 AM...

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Biconnectivity 3/13/2006 1:49 AM 1 3/13/2006 1:49 AM Biconnectivity 1 Biconnectivity SEA PVD MIA SNA ORD FCO 3/13/2006 1:49 AM Biconnectivity 2 Outline and Reading Definitions (§6.3.2) ± Separation vertices and edges ± Biconnected graph ± Biconnected components ± Equivalence classes ± Linked edges and link components Algorithms (§6.3.2) ± Auxiliary graph ± Proxy graph
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Biconnectivity 3/13/2006 1:49 AM 2 3/13/2006 1:49 AM Biconnectivity 3 Separation Edges and Vertices Definitions ± Let G be a connected graph ± A separation edge of G is an edge whose removal disconnects G ± A separation vertex of G is a vertex whose removal disconnects G Applications ± Separation edges and vertices represent single points of failure in a network and are critical to the operation of the network Example ± DFW, LGA and LAX are separation vertices ± (DFW,LAX) is a separation edge ORD PVD MIA DFW SFO LAX LGA HNL 3/13/2006 1:49 AM Biconnectivity 4 Biconnected Graph Equivalent definitions of a biconnected graph G ± Graph G has no separation edges and no separation vertices ± For any two vertices u and v of G , there are two disjoint simple paths between u
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Biconnectivity-new-handouts-2 - Biconnectivity 1:49 AM...

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