Efficient splitting off algorithms for graphs

Abstract

Splitting off is a powerful tool for proving theorems and developing polynomial-Time algorithms on graphs, especially for edge-connectivity problems. We present efficient algorithms for splitting off, leading to efficient algorithms for connectivity problems. We improve previous algorithms (based on submodular flow) to find a k-edge-connected orientation of an undirected graph or multigraph. We also improve the best bounds for the edge connectivity augmentation problem for undirected and directed multigraphs, and for the local connectivity augmentation problem on undirected graphs and multi- graphs, each by a factor n. We also give efficient al-gorithms for finding a well-balanced orientation of an undirected graph or multigraph. Our approach uses a graph transformation that allows efficient computation of cuts that are variants of the minimum s, t-cut.