Parallel Algorithms for Computing Jaccard Weights on Graphs using Linear Algebra

Jaccard similarity between a pair of vertices in a graph measures the relative overlap among their adjacent vertices. This metric is used to estimate the strength of existing edges and predict new edges between pairs of disconnected vertices. Computing Jaccard similarity for all pairs of vertices or for all edges is computationally expensive. Existing sequential and parallel algorithms are either too slow or do not scale well for large scale graphs. We present a shared-memory parallel al-gorithm for computing Jaccard weights. Our algorithm relies on sparse linear algebraic operations that utilize masking, semirings, vector iterators, and other GraphBLAS features for performance. Our implementation, albeit simple, outperforms recent state-of-the-art implementations by a factor of up to 20 x and exhibits an average speedup of 9 x.