An Efficient Approach to Finding Dense Temporal Subgraphs

Dense subgraph discovery has proven useful in various applications of temporal networks. We focus on a special class of temporal networks whose nodes and edges are kept fixed, but edge weights regularly vary with timestamps. However, finding dense subgraphs in temporal networks is non-trivial, and its state of the art solution uses a filter-and-verification framework that is not scalable on large temporal networks. In this study, we propose a highly efficient approach to finding dense subgraphs in large temporal networks with T timestamps. (1) We first develop a statistics-driven approach that employs hidden statistics to identifying k time intervals, instead of $T(T + 1)/2$ ones ( $k$ is typically much smaller than T), which strikes a balance between quality and efficiency. (2) After proving that the problem has no constant factor approximation algorithms, we design better heuristic algorithms to attack the problem, by connecting finding dense subgraphs with a variant of the Prize Collecting Steiner Tree problem. (3) Finally, we have conducted an extensive experimental study to verify that our approach is both effective and efficient.