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Wing and Tip decomposition construct a hierarchy of butterfly-dense edge andvertex induced bipartite subgraphs, respectively. They have applications inseveral domains including e-commerce, recommendation systems and documentanalysis. Existing decomposition algorithms use a bottom-up approach thatconstructs the hierarchy in an increasing order of subgraph density. Theyiteratively peel the entities with minimum butterfly count i.e. remove themfrom the graph and update the butterfly count of other entities. However, theamount of butterflies in large bipartite graphs makes bottom-up peelingcomputationally demanding. Furthermore, the strict order of peeling entitiesresults in a numerous sequentially dependent iterations, which makesparallelization challenging.  In this paper, we propose a novel Parallel Bipartite Network peelinG (PBNG)framework which adopts a two-phased peeling approach to relax the order ofpeeling, and in turn, reduce synchronization. The first phase divides thedecomposition hierarchy into several partitions using very few peelingiterations. The second phase concurrently processes these partitions togenerate the final hierarchy, and requires no global synchronization. Thetwo-phased peeling further enables batching optimizations that dramaticallyimprove the computational efficiency.  We empirically evaluate PBNG using several real-world bipartite graphs.Compared to the state-of-the-art frameworks and decomposition algorithms, PBNGachieves up to four orders of magnitude reduction in synchronization and twoorders of magnitude speedup, respectively. We also present the firstdecomposition results of some of the largest public real-world datasets, whichPBNG can peel in few minutes but existing algorithms fail to process even inseveral days.

Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery