Dynamic Structural Clustering Unleashed: Flexible Similarities, Versatile Updates and for All Parameters

We study structural clustering on graphs in dynamic scenarios, where graphs can be updated by arbitrary insertions or deletions of edges/vertices. Our goal is to efficiently compute structural clustering results under three conditions: 1) for any clustering parameters ε and μ provided on the fly, 2) for arbitrary graph update patterns, and 3) for all typical similarity measurements. To achieve this, we propose an algorithm named VD-STAR that is much simpler yet more efficient than state of the art. With a theoretical guarantee on clustering result's quality, VD-STAR can produce clustering results with up to 99.9% accuracy. Moreover, VD-STAR is easy to implement as it just needs to maintain sorted linked lists and hash tables, making it highly deployable in practice. Most importantly, VD-STAR improves the expected per-update time bound from state-of-the-art O(log2 n), which relies on specific assumption on update pattern, to O(log n) amortized in expectation without any assumption on update pattern. We further design two variants of VD-STAR to enhance its empirical performance. Experimental results show that our algorithms consistently outperform state-of-the-art competitors by up to 9,315 times in update time across nine real datasets, while maintaining similar update time and memory usage.