## Biconnectivity Approximations and Graph Carvings (1994)

Citations: | 84 - 3 self |

### BibTeX

@MISC{Khuller94biconnectivityapproximations,

author = {Samir Khuller and Uzi Vishkin},

title = {Biconnectivity Approximations and Graph Carvings},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2-connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified) ? Unfortunately, the problem is known to be NP -hard. We consider the problem of finding a better approximation to the smallest 2-connected subgraph, by an efficient algorithm. For 2-edge connectivity our algorithm guarantees a solution that is no more than 3 2 times the optimal. For 2-vertex connectivity our algorithm guarantees a solution that is no more than 5 3 times the optimal. The previous best approximation factor is 2 for each of these problems. The new algorithms (and their analyses) depend upon a structure called a carving of a graph, which is of independent interest. We show that approximating the optimal solution to within an additive constant is NP -hard as well. We also consider the case where the graph has edge weigh...