Approximating the Smallest 2-Vertex-Connected Spanning Subgraph via Low-High Orders

Let G = (V,E) be a 2-vertex-connected directed graph with m edges and n vertices. We consider the problem of approximating the smallest 2-vertex connected spanning subgraph (2VCSS) of G, and provide new efficient algorithms for this problem based on a clever use of low-high orders. The best previously known algorithms were able to compute a 3/2-approximation in O(m √ n+n2) time, or a 3-approximation faster in linear time. In this paper, we present a linear-time algorithm that achieves a better approximation ratio of 2, and another algorithm that matches the previous 3/2-approximation in O(m √ n+ n2) time. We conducted a thorough experimental evaluation of all the above algorithms on a variety of input graphs. The experimental results show that both our two new algorithms perform well in practice. In particular, in our experiments the new 3/2-approximation algorithm was always faster than the previous 3/2-approximation algorithm, while their two approximation ratios were close. On the other side, our new linear-time algorithm yielded consistently better approximation ratios than the previously known linear-time algorithm, at the price of a small overhead in the running time. 1998 ACM Subject Classification E.1 [Data Structures] Graphs and Networks, Trees, G.2.2 [Graph Theory] Graph Algorithms