@article {15213,
title = {Biconnectivity approximations and graph carvings},
journal = {Journal of the ACM (JACM)},
volume = {41},
year = {1994},
month = {1994/03//},
pages = {214 - 235},
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 weights. For this case, we show that an approximation factor of 2 is possible in polynomial time for finding a k-edge connected spanning subgraph. This improves an approximation factor of 3 for k = 2, due to Frederickson and Ja{\textasciiacute}Ja{\textasciiacute} [1981], and extends it for any k (with an increased running time though).
},
keywords = {biconnectivity, connectivity, sparse subgraphs},
isbn = {0004-5411},
doi = {10.1145/174652.174654},
url = {http://doi.acm.org/10.1145/174652.174654},
author = {Khuller, Samir and Vishkin, Uzi}
}