Computing the 4-Edge-Connected Components of a Graph: An Experimental Study

The notions of edge-cuts and 푘-edge-connected components are fundamental in graph theory with numerous practical applications. Very recently, the first linear-time algorithms for computing all the 3-edge-cuts and the 4-edge-connected components of a graph have been introduced. In this article, we present carefully engineered implementations of these algorithms and evaluate their efficiency in practice, by performing a thorough empirical study using both real-world graphs taken from a variety of application areas, as well as artificial graphs. To the best of our knowledge, this is the first experimental study for these problems, which highlights the merits and weaknesses of each technique. Furthermore, 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 is implementable in the pointer-machine model of computation.