We study the temporal k-core component search (TCCS), which outputs the k-core containing the query vertex in the snapshot over an arbitrary query time window in a temporal graph. The problem has been shown to be critical for tasks such as contact tracing, fault diagnosis, and financial forensics. The state-of-the-art EF-Index designs a separated forest structure for a set of carefully selected windows, incurring quadratic preprocessing time and large redundant storage. Our method introduces the ECB-forest, a compact edge-centric binary forest that captures k-core of any arbitrary query vertex over time. In this way, a query can be processed by searching a connected component in the forest. We develop an efficient algorithm for index construction. Experiments on real-world temporal graphs show that our method significantly improves the index size and construction cost (up to 100x faster on average) while maintaining the high query efficiency.
@article{arxiv.2508.18151,
title = {Accelerating Historical K-Core Search in Temporal Graphs},
author = {Zhuo Ma and Dong Wen and Kaiyu Chen and Yixiang Fang and Xuemin Lin and Wenjie Zhang},
journal= {arXiv preprint arXiv:2508.18151},
year = {2025}
}