Bermuda: An Efficient MapReduce Triangle Listing Algorithm for Web-Scale Graphs

Triangle listing plays an important role in graph analysis and has numerous graph mining applications. With the rapid growth of graph data, distributed methods for listing triangles over massive graphs are urgently needed. Therefore, the triangle listing problem has been studied in several distributed infrastructures including MapReduce. However, existing algorithms suffer from generating and shuffling huge amounts of intermediate data, where interestingly, a large percentage of this data is redundant. Inspired by this observation, we present the "Bermuda" method, an efficient MapReducebased triangle listing technique for massive graphs.

Different from existing approaches, Bermuda effectively reduces the size of the intermediate data via redundancy elimination and sharing of messages whenever possible. As a result, Bermuda achieves orders-of-magnitudes of speedup and enables processing larger graphs that other techniques fail to process under the same resources. Bermuda exploits the locality of processing, i.e., in which reduce instance each graph vertex will be processed, to avoid the redundancy of generating messages from mappers to reducers. Bermuda also proposes novel message sharing techniques within each reduce instance to increase the usability of the received messages. We present and analyze several reduce-side caching strategies that dynamically learn the expected access patterns of the shared messages, and adaptively deploy the appropriate technique for better sharing. Extensive experiments conducted on real-world large-scale graphs show that Bermuda speeds up the triangle listing computations by factors up to 10x. Moreover, with a relatively small cluster, Bermuda can scale up to large datasets, e.g., ClueWeb graph dataset (688GB), while other techniques fail to finish.