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 O(∆ · d), where ∆ 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% (±1%). Finally, the incremental summarization algorithm outperforms the batch algorithm even when using fewer cores.