External connected components

Abstract

Algorithms are considered for the external connected-components problem. The main contribution is an algorithm which for a graph with n nodes and m edges has an expected running time bounded by O(m·log log n) when randomizing the node indices. A blocked version of this algorithm, which is perfectly suited for external application, handles bundles of W nodes at a time. For random graphs, the running time of this algorithm is bounded by O(log log(n2/(m · W)) · m). A special case of the algorithm solves the list-ranking and tree-rooting problem. The running time of this algorithm is linear in the number of involved nodes, independently of their arrangement. © Springer-Verlag Berlin Heidelberg 2004.