Near-optimal and practical algorithms for graph scan statistics

Abstract

Scan statistics is a popular approach used for detecting "hotspots" and "anomalies" in spatio-temporal and network data. This methodology involves maximizing a score function over all connected subgraphs, which is NP-hard in general. A number of heuristics have been proposed for these problems, but they do not provide any quality guarantees. In this paper, we develop a framework for designing algorithms for optimizing a large class of scan statistics for networks, subject to connectivity constraints. Our algorithms run in time that scales linearly on the size of the graph and depends on a parameter we call the "effective solution size", while providing rigorous approximation guarantees. In contrast, most prior methods have super-linear running times in terms of graph size. Extensive empirical evidence demonstrates the effectiveness and efficiency of our proposed algorithms in comparison with state-of-the-art methods. Our approach improves on the performance relative to all prior methods, giving up to over 25% increase in the score. Further, our algorithms scale to networks with up to a million nodes, which is 1-2 orders of magnitude larger than all prior applications.