Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery

Abstract

Wing and Tip decomposition are motif-based analytics for bipartite graphs that construct a hierarchy of butterfly (2,2-biclique) dense edge and vertex induced subgraphs, respectively. They have applications in several domains, including e-commerce, recommendation systems, document analysis, and others. Existing decomposition algorithms use a bottom-up approach that constructs the hierarchy in an increasing order of the subgraph density. They iteratively select the edges or vertices with minimum butterfly count peel, i.e., remove them along with their butterflies. The amount of butterflies in real-world bipartite graphs makes bottom-up peeling computationally demanding. Furthermore, the strict order of peeling entities results in a large number of sequentially dependent iterations. Consequently, parallel algorithms based on bottom up peeling incur heavy synchronization and poor scalability. In this article, we propose a novel Parallel Bipartite Network peelinG (PBNG) framework that adopts a two-phased peeling approach to relax the order of peeling, and in turn, dramatically reduce synchronization. The first phase divides the decomposition hierarchy into few partitions and requires little synchronization. The second phase concurrently processes all partitions to generate individual levels of the hierarchy and requires no global synchronization. The two-phased peeling further enables batching optimizations that dramatically improve the computational efficiency of PBNG. We empirically evaluate PBNG using several real-world bipartite graphs and demonstrate radical improvements over the existing approaches. On a shared-memory 36 core server, PBNG achieves up to 19.7× self-relative parallel speedup. Compared to the state-of-the-art parallel framework ParButterfly, PBNG reduces synchronization by up to 15,260× and execution time by up to 295×. Furthermore, it achieves up to 38.5× speedup over state-of-the-art algorithms specifically tuned for wing decomposition. Our source code is made available at https://github.com/kartiklakhotia/RECEIPT.