Biblio

Motivated by networked systems in which the functionality of the network depends on vertices in the network being within a bounded distance T of each other, we study the length-bounded multicut problem: given a set of pairs, find a minimum-size set of edges whose removal ensures the distance between each pair exceeds T . We introduce the first algorithms for this problem capable of scaling to massive networks with billions of edges and nodes: three highly scalable algorithms with worst-case performance ratios. Furthermore, one of our algorithms is fully dynamic, capable of updating its solution upon incremental vertex / edge additions or removals from the network while maintaining its performance ratio. Finally, we show that unless NP ⊆ BPP, there is no polynomial-time, approximation algorithm with performance ratio better than Omega (T), which matches the ratio of our dynamic algorithm up to a constant factor.

Outlier detection is a fundamental data science task with applications ranging from data cleaning to network security. Recently, a new class of outlier detection algorithms has emerged, called contextual outlier detection, and has shown improved performance when studying anomalous behavior in a specific context. However, as we point out in this article, such approaches have limited applicability in situations where the context is sparse (i.e., lacking a suitable frame of reference). Moreover, approaches developed to date do not scale to large datasets. To address these problems, here we propose a novel and robust approach alternative to the state-of-the-art called RObust Contextual Outlier Detection (ROCOD). We utilize a local and global behavioral model based on the relevant contexts, which is then integrated in a natural and robust fashion. We run ROCOD on both synthetic and real-world datasets and demonstrate that it outperforms other competitive baselines on the axes of efficacy and efficiency. We also drill down and perform a fine-grained analysis to shed light on the rationale for the performance gains of ROCOD and reveal its effectiveness when handling objects with sparse contexts.