On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We present the first shared-memory parallel algorithm for incremental graph connectivity that is both provably work-efficient and has polylogarithmic parallel depth. We also present a simpler algorithm with slightly worse theoretical properties, but which is easier to implement and has good practical performance. Our experiments show a throughput of hundreds of millions of edges per second on a 20-core machine.

The incremental graph connectivity (IGC) problem is to maintain a data structure that can quickly answer whether two given vertices in a graph are connected, while allowing more edges to be added to the graph. IGC is a fundamental problem and can be solved efficiently in the sequential setting using a solution to the classical union-find problem. However, sequential solutions are not sufficient to handle modern-day large, rapidly-changing graphs where edge updates arrive at a very high rate. We present the first shared-memory parallel data structure for union-find (equivalently, IGC) that is both provably work-efficient (ie, performs no more work than the best sequential counterpart) and has polylogarithmic parallel depth. We also present a simpler algorithm with slightly worse theoretical properties, but which is easier to implement and has good practical performance. Our experiments on large graph streams with various degree distributions show that it has good practical performance, capable of processing hundreds of millions of edges per second using a 20-core machine.

With the growing popularity of wearable devices, the ability to utilize physiological data collected from these devices to predict the wearer's mental state such as mood and stress suggests great clinical applications, yet such a task is extremely challenging. In this paper, we present a general platform for personalized predictive modeling of behavioural states like students' level of stress. Through the use of Auto-encoders and Multitask learning we extend the prediction of stress to both sequences of passive sensor data and high-level covariates. Our model outperforms the state-ofthe-art in the prediction of stress level from mobile sensor data, obtaining a 45.6% improvement in F1 score on the StudentLife dataset.