A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By contrast, the previously best-known algorithms make multiple passes over the graph to decompose it into its 2-edge-connected components or 2-vertex-connected components, then its 3-edge-connected components or 3-vertex-connected components, and then construct a cactus representation for the 2-cuts to generate the auxiliary subgraphs for the 3-edge-connected components.

翻译：本文提出一种线性时间算法，用于生成连通多重图的三边连通分量所需的辅助子图。该算法采用创新的图收缩操作，仅需对图进行一次遍历。与此相对，此前最优算法需对图进行多次遍历：先将其分解为二边连通分量或二顶点连通分量，再分解为三边连通分量或三顶点连通分量，接着为二割集构建仙人掌表示，最后生成三边连通分量的辅助子图。