Mining Heavy Subgraphs in Time-Evolving Networks

Networks from different genres are not static entities, but exhibit dynamic behavior. The congestion level of links in transportation networks varies in time depending on the traffic. Similarly, social and communication links are employed at varying rates as information cascades unfold. In recent years there has been an increase of interest in modeling and mining dynamic networks. However, limited attention has been placed in high-scoring sub graph discovery in time-evolving networks. We define the problem of finding the highest-scoring temporal sub graph in a dynamic network, termed Heaviest Dynamic Sub graph (HDS). We show that HDS is NP-hard even with edge weights in {-1,1} and devise an efficient approach for large graph instances that evolve over long time periods. While a naive approach would enumerate all O(t²) sub-intervals, our solution performs an effective pruning of the sub-interval space by considering O(t·log(t)) groups of sub-intervals and computing an aggregate of each group in logarithmic time. We also define a fast heuristic and a tight upper bound for approximating the static version of HDS, and use them for further pruning the sub-interval space and quickly verifying candidate sub-intervals. We perform an extensive experimental evaluation of our algorithm on transportation, communication and social media networks for discovering sub graphs that correspond to traffic congestions, communication overflow and localized social discussions. Our method is two orders of magnitude faster than a naive approach and scales well with network size and time length.