Time and Memory Efficient Algorithm for Structural Graph Summaries over Evolving Graphs

Existing graph summarization algorithms are tailored to specific graph summary models, only support one-time batch computation, are designed and implemented for a specific task, or are evaluated using static graphs. Our novel, incremental, parallel algorithm addresses all of these shortcomings. We support infinitely many structural graph summary models defined in a formal language. All graph summaries can be updated in time $\mathcal{O}(\Delta \cdot d^k)$, where $\Delta$ is the number of additions, deletions, and modifications to the input graph, $d$ is its maximum degree, and $k$ is the maximum distance in the subgraphs considered while summarizing. We empirically evaluate the performance of our incremental algorithm on benchmark and real-world datasets. Overall our experiments show that, for commonly used summary models and datasets, the incremental summarization algorithm almost always outperforms its batch counterpart, even when about $50\%$ of the graph database changes. Updating the summaries of the real-world DyLDO-core dataset with our incremental algorithm is $5$ to $44$~times faster than computing a new summary, when using four cores. Furthermore, the incremental computations require a low memory overhead of only $8\%$ ($\pm 1\%$). Finally, the incremental summarization algorithm outperforms the batch algorithm even when using fewer cores.