Graph Summarization: Compactness Meets Efficiency

As the volume and ubiquity of graphs increase, a compact graph representation becomes essential for enabling efficient storage, transfer, and processing of graphs. Given a graph, the graph summarization problem asks for a compact representation that consists of a summary graph and the corrections, such that we can recreate the original graph from the representation exactly. Although this problem has been studied extensively, the existing works either trade summary compactness for efficiency, or vice versa. In particular, a well-known greedy method provides the most compact summary but incurs prohibitive time cost, while the state-of-the-art algorithms with practical overheads are more than 20% behind in summary compactness in our comparison with the greedy method.

This paper presents Mags and Mags-DM, two algorithms that aim to bridge the compactness and efficiency in graph summarization. Mags adopts the existing greedy paradigm that provides state-of-the-art compactness, but significantly improves its efficiency with a novel algorithm design. Meanwhile, Mags-DM follows a different paradigm with practical efficiency and overcomes its limitations in compactness. Moreover, both algorithms can support parallel computing environments. We evaluate Mags and Mags-DM on graphs up to billion-scale and demonstrate that they achieve state-of-the-art in both compactness and efficiency, rather than in one of them. Compared with the method that offers state-of-the-art compactness, Mags and Mags-DM have a small difference (< 0.1% and < 2.1%) in compactness. For efficiency, Mags is on average 11.1x and 4.2x faster than the two state-of-the-art algorithms with practical overheads, while Mags-DM can further reduce the running time by 13.4x compared with Mags. This shows that graph summarization algorithms can be made practical while still offering a compact summary.

CCS Concepts: • Theory of computation → Graph algorithms analysis.