lec26 - CS C341 / I S C361 Data Structures & Algorithms...

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CS C341 / I S C361 GRAPH ALGORITHMS Undirected Graphs Biconnected Graphs Bi-connected Components Properties of Biconnectivity Cycle Relation and Equivalence classes Algorithm for finding Biconnected components 1 02/07/11 Sundar B. CSIS, BITS, Pilani
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BI-CONNECTED COMPONENTS Motivation: Is there is a single point of failure in a computer network? i.e. is there an edge whose removal disconnects G? if so, such an edge is referred to as separation edge of G OR is there a vertex whose removal disconnects G? if so, such a vertex is referred to as separation vertex of G 02/07/11 2 Sundar B. CSIS, BITS, Pilani A C B D E G F H
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BI-CONNECTED COMPONENTS A connected graph G is biconnected if, for any two vertices u and v, there are two disjoint paths between u and v: i.e two paths sharing no common edges or vertices 02/07/11 3 Sundar B. CSIS, BITS, Pilani A C B D E G F H
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BI-CONNECTED COMPONENTS A biconnected component of G is a subgraph G’ such that: G’ is biconnected and adding any additional vertex / edges of G would make it not biconnected OR G’ is a single separation edge of G and its endpoints 02/07/11 4 Sundar B. CSIS, BITS, Pilani A C B D E F
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BI-CONNECTED COMPONENTS Properties of Bi-connectivity: If G is biconnected, then G has one biconnected
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lec26 - CS C341 / I S C361 Data Structures & Algorithms...

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