Batch Dynamic Algorithm to Find k-Cores and Hierarchies

TL;DR

This paper introduces a new batch dynamic algorithm for efficiently maintaining k-core decompositions and hierarchies in rapidly changing graphs, enabling fast core queries suitable for interactive applications.

Contribution

It presents a novel dynamic batch algorithm utilizing the Shell Tree Index to improve efficiency in maintaining core decompositions in dynamic graphs.

Findings

Achieves over 100x speedup on 1 million edge batches compared to edge-by-edge processing.

Enables core queries on rapidly changing graphs to be performed quickly enough for interactive use.

Demonstrates effectiveness on various real-world graph datasets.

Abstract

Finding $k$-cores in graphs is a valuable and effective strategy for extracting dense regions of otherwise sparse graphs. We focus on the important problem of maintaining cores on rapidly changing dynamic graphs, where batches of edge changes need to be processed quickly. Prior batch core algorithms have only addressed half the problem of maintaining cores, the problem of maintaining a core decomposition. This finds vertices that are dense, but not regions; it misses connectivity. To address this, we bring an efficient index from community search into the core domain, the Shell Tree Index. We develop a novel dynamic batch algorithm to maintain it that improves efficiency over processing edge-by-edge. We implement our algorithm and experimentally show that with it core queries can be returned on rapidly changing graphs quickly enough for interactive applications. For 1 million edge batches, on many graphs we run over $100\times$ faster than processing edge-by-edge while remaining under re-computing from scratch.