Improving biconnectivity approximation via local optimization
Ka Wong Chong, Tak‐Wah Lam · Symposium on Discrete Algorithms · 1996
The problem of finding the minimum biconnected spanning subgraph of an undirected graph is NP-hard. A lot of effort has been made to find biconnected spanning subgraphs that approximate to the minimum one as close as possible. Recently, new polynomial-time (sequential) approximation algorithms have been devised to improve the approximation factor from 2 to 5/3 , then 3/2, while NC algorithms have also been known to achieve 7/4 + {epsilon}. This paper presents a new technique which can be used to further improve parallel approximation factors to 5/3 + {epsilon}. In the sequential context, the technique reveals an algorithm with a factor of {alpha} + 1/5, where a is the approximation factor of any 2-edge connectivity approximation algorithm.