Chatterjee, Gmyr, and Pandurangan [PODC 2020] recently introduced the notion of awake complexity for distributed algorithms, which measures the number of rounds in which a node is awake. In the other rounds, the node is sleeping and performs no computation or communication. Measuring the number of awake rounds can be of significance in many settings of distributed computing, e.g., in sensor networks where energy consumption is of concern.In that paper, Chatterjee et al. provide an elegant randomized algorithm for the Maximal Independent Set (MIS) problem that achieves an O(1) node-averaged awake complexity. That is, the average awake time among the nodes is O(1) rounds. However, to achieve that, the algorithm sacrifices the more standard round complexity measure from the well-known O(log n) bound of MIS, due to Luby [STOC'85], to O(log 3.41 n) rounds.Our first contribution is to present a simple randomized distributed MIS algorithm that, with high probability, has O(1) node-averaged awake complexity and O(log n) worst-case round complexity. Our second, and more technical contribution, is to show algorithms with the same O(1) node-averaged awake complexity and O(log n) worst-case round complexity for (1 + ε)-approximation of maximum matching and (2+ε)-approximation of minimum vertex cover, where ε denotes an arbitrary small positive constant.

Objective. Learning to classify cardiac abnormalities requires large and high-quality labeled datasets, which is a challenge in medical applications. Small datasets from various sources are often aggregated to meet this requirement, resulting in a final dataset prone to label noise owing to inter- and intra-observer variability, and different expertise. It is well known that label noise can affect the performance and generalizability of the trained models. In this work, we explore the impact of label noise and self-learning label correction on the classification of cardiac abnormalities on large heterogeneous datasets of electrocardiogram (ECG) signals. Approach. A state-of-the-art self-learning multi-class label correction method for image classification is adapted to learn a multi-label classifier for electrocardiogram signals. We evaluated our performance using 5-fold cross-validation on the publicly available PhysioNet/Computing in Cardiology (CinC) 2021 Challenge data, with full and reduced sets of leads. Due to the unknown label noise in the testing set, we tested our approach on the MNIST dataset. We investigated the performance under different levels of structured label noise for both datasets. Main results. Under high levels of noise, the cross-validation results of self-learning label correction showed an improvement of approximately 3% in the Challenge score for the PhysioNet/CinC 2021 Challenge dataset and, an improvement in accuracy of 5$\%$ and reduction of the expected calibration error of 0.03 for the MNIST dataset. We demonstrate that self-learning label correction can be used to effectively deal with the presence of unknown label noise, also when using a reduced number of ECG leads.

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