A Fast Edge-Splitting Algorithm in Edge-Weighted Graphs

摘要

Let H be a graph with a designated vertex s, where edges are weighted by nonnegative reals. Splitting edges e = {u, s} and e' = {s, v} at s is an operation that reduces the weight of each of e and e' by a real δ > 0 while increasing the weight of edge {u, v} by 6. It is known that all edges incident to s can be split off while preserving the edge-connectivity of H and that such a complete splitting is used to solve many connectivity problems. In this paper, we give an O(mn + n~2 log n) time algorithm for finding a complete splitting in a graph with n vertices and m edges.