A simple linear-time algorithm for generating auxiliary 3-edge-connected subgraphs

TL;DR

This paper introduces a novel linear-time algorithm for efficiently generating auxiliary subgraphs for 3-edge-connected components in connected multigraphs, improving over previous multi-pass methods.

Contribution

The paper presents an innovative graph contraction-based algorithm that operates in a single pass, simplifying and speeding up the process of finding 3-edge-connected components.

Findings

Algorithm runs in linear time

Reduces the number of graph passes needed

Simplifies the process of generating auxiliary subgraphs

Abstract

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.