Efficient Edge Splitting-Off Algorithms Maintaining All-Pairs Edge-Connectivities

We present new edge splitting-off results maintaining all-pairs edge-connectivities of an undirected graph. We first give an alternate proof of Mader’s theorem, and use it to obtain a deterministic Õ(m + rmax · n2)-time complete edge splitting-off algorithm for unweighted graphs, where rmax denotes the maximum edge-connectivity requirement. This improves upon the best known algorithm by Gabow by a factor of Ω̃(n). We then prove a new structural property, and use it to further speed up the algorithm to obtain a randomized Õ(m+ rmax ·n)-time algorithm. These edge splitting-off algorithms can be used directly to speed up various graph algorithms.