Improved Linear-Time Algorithm for Computing the $4$-Edge-Connected Components of a Graph

TL;DR

This paper introduces a simplified, elementary, linear-time algorithm for identifying 4-edge-connected components in undirected graphs, making the process more efficient and easier to implement.

Contribution

It provides a new, straightforward linear-time algorithm for computing 4-edge-connected components using only elementary data structures.

Findings

Algorithm runs in linear time

Uses only elementary data structures

Easier to implement and understand

Abstract

We present an improved algorithm for computing the $4$-edge-connected components of an undirected graph in linear time. The new algorithm uses only elementary data structures, and it is simple to describe and to implement in the pointer machine model of computation.