Massive graph triangulation

Abstract

This paper studies I/O-efficient algorithms for settling the classic triangle listing problem, whose solution is a basic operator in dealing with many other graph problems. Specifically, given an undirected graph G, the objective of triangle listing is to find all the cliques involving 3 vertices in G. The problem has been well studied in internal memory, but remains an urgent difficult challenge when G does not fit in memory, rendering any algorithm to entail frequent I/O accesses. Although previous research has attempted to tackle the challenge, the state-of-the-art solutions rely on a set of crippling assumptions to guarantee good performance. Motivated by this, we develop a new algorithm that is provably I/O and CPU efficient at the same time, without making any assumption on the input G at all. The algorithm uses ideas drastically different from all the previous approaches, and outperformed the existing competitors by a factor over an order of magnitude in our extensive experimentation.