Efficient Graph Summarization using Weighted LSH at Billion-Scale

Summarizing graphs is of paramount importance due to diverse applications of large-scale graph analysis. A popular family of summarization methods is the group-based approach. The general idea consists of merging nodes of the original graph into supernodes of the summary graph, encoding original edges into superedges/correction set edges, and dropping certain superedges or correction set edges (for lossy summarization). The current state of the art has several steps in its computation that are serious bottlenecks in terms of running time and scalability. In this work, we propose algorithm LDME, a correction set based graph summarization algorithm that produces compact output representations in a fast and scalable manner. To achieve this, we introduce (1) weighted locality sensitive hashing to drastically reduce the number comparisons required to find good node merges, (2) an efficient way to compute the best quality merges that produces more compact outputs, and (3) a new sort-based encoding algorithm that is faster and more robust. More interestingly, our algorithm provides performance tuning settings to allow the option of trading compression for running time. On high compression settings, LDME achieves compression equal to or better than the state of the art with up to 53x speedup in running time. On high speed settings, LDME achieves up to two orders of magnitude speedup with only slightly lower compression.