iTri: Index-based triangle listing in massive graphs

Triangle listing is a basic operator when dealing with many graph problems. However, in-memory algorithms do not work well with recently developed massive graphs such as social networks because these graphs cannot be accommodated in the memory. Thus, external memory-based algorithms have been proposed recently, but these approaches still require frequent multiple scans of the whole graph on the disk and large volumes of calculations are performed that involve the whole graph during every iteration. In this study, we propose a novel index-based method for listing triangles in massive graphs. First, we present new notions for the vertex range index and potential cone vertex index. Next, we propose an index join-based triangle listing algorithm. Our method accesses the indexed data asynchronously and joins them to list triangles using a multi-threaded parallel processing technique. Based on experiments, we demonstrate that our algorithm outperforms the state-of-the-art solution methods by three to eight times in terms of the wall clock time.