Mining Heavy Temporal Subgraphs: Fast Algorithms and Applications

Anomaly detection is a fundamental problem in dynamic networks. In this paper, we study an approach for identifying anomalous subgraphs based on the Heaviest Dynamic Subgraph (HDS) problem. The HDS in a time-evolving edge-weighted graph consists of a pair containing a subgraph and sub-interval whose sum of edge weights is maximized. The HDS problem in a static graph is equivalent to the Prize Collecting Steiner Tree (PCST) problem with the Net-Worth objective-this is a very challenging problem, in general, and numerous heuristics have been proposed. Prior methods for the HDS problem use the PCST solution as a heuristic, and run in time quadratic in the size of the graph. As a result, they do not scale well to large instances. In this paper, we develop a new approach for the HDS problem, which combines rigorous algorithmic and practical techniques and has much better scalability. Our algorithm is able to extend to other variations of the HDS problem, such as the problem of finding multiple anomalous regions. We evaluate our algorithms in a diverse set of real and synthetic networks, and we find solutions with higher score and better detection power for anomalous events compared to earlier heuristics.