Implementation of a Linear Expected-Time Algorithm for Finding Connected Components

We describe a robust and efficient implementation of the Karp and Tarzan [4] algorithm for finding the connected components of an undirected graph. The algorithm achieves to find the connected components of a graph G = (V,E) in O(|V|) expected time. The implementation of the algorithm (called GCOMPONENTS) is based on the LEDA library of efficient data types and algorithms [5,6,7]. This is the first expected-time algorithm for graph connectivity implemented in LEDA. Note that the best algorithm for finding the connected components in a graph requires time O(|V|+|E|) in the worst case. Such an algorithm called COMPONENTS, is implemented in LEDA.