Biconnectivity - Biconnectivity 4/1/2003 8:36 AM Outline...

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4/1/2003 8:36 AM Biconnectivity 1 Biconnectivity SEA PVD MIA SNA ORD FCO 4/1/2003 8:36 AM Biconnectivity 2 Outline and Reading Definitions ± Separation vertices and edges ± Biconnected graph ± Biconnected components ± Equivalence classes ± Linked edges and link components Algorithms ± Auxiliary graph ± Proxy graph 4/1/2003 8:36 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 4/1/2003 8:36 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 and v (i.e., two simple paths between u and v that share no other vertices or edges) ± For any two vertices u and v of G , there is a simple cycle containing u and v Example ORD PVD MIA DFW SFO LAX LGA HNL 4/1/2003 8:36 AM Biconnectivity
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This note was uploaded on 02/02/2012 for the course CS 251 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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Biconnectivity - Biconnectivity 4/1/2003 8:36 AM Outline...

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