Parallel Algorithms for Butterfly Computations

Abstract

Butterflies are the smallest non-trivial subgraph in bipartite graphs, and therefore having efficient computations for analyzing them is crucial to improving the quality of certain applications on bipartite graphs. In this paper, we design a framework called ParButterfly that produces new parallel algorithms for the following problems on processing butterflies: global counting, per-vertex counting, per-edge counting, tip decomposition (vertex peeling), and wing decomposition (edge peeling). The main component of these algorithms is combining wedges incident on subsets of vertices, and our framework allows us to use different methods for wedge aggregation, including combining via sorting, hashing, histogramming, and batching. Moreover, ranking the vertices can speed up butterfly counting, as we only need to consider wedges formed by a particular ordering of the vertices. ParButterfly supports different ways to rank the vertices, including side ordering, approximate and exact degree ordering, and approximate and exact complement coreness ordering. For counting, ParButterfly also supports both exact computation as well as approximate computation via graph sparsification. We prove strong theoretical guarantees on the work and give parallel running times of the algorithms as obtained in our framework.We perform a comprehensive evaluation of all of the algorithms obtained from ParButterfly on a collection of real-world bipartite graphs using a 48-core machine. Our algorithms obtain significant parallel speedup, outperforming the fastest sequential algorithms by up to 13.6x with a self-relative speedup of up to 38.5x. Compared to general subgraph counting solutions, we are orders of magnitude faster. arXiv:1907.08607v1 [cs.DC] 19 Jul 2019 2 The arboricity of a graph is defined to be the minimum number of disjoint forests that a graph can be partitioned into.

Parallel Clique Counting and Peeling Algorithms

“…In practice, we use the bucketing structure by Dhulipala et al [16]. However, for theoretical purposes, we use the batch-parallel Fibonacci heap by Shi and Shun [49] Graph Storage. In our implementations, we store our graphs in compressed sparse row (CSR) format, which requires O(m + n) space.…”

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