This paper introduces a family of learning-augmented algorithms for online knapsack problems that achieve near Pareto-optimal consistency-robustness trade-offs through a simple combination of trusted learning-augmented and worst-case algorithms. Our approach relies on succinct, practical predictions—single values or intervals estimating the minimum value of any item in an offline solution. Additionally, we propose a novel fractional-to-integral conversion procedure, offering new insights for online algorithm design.

As large-scale data processing workloads continue to grow, their carbon footprint raises concerns. Prior research on carbon-aware schedulers has focused on shifting computation to align with the availability of low-carbon energy, but these approaches assume that each task can be executed independently. In contrast, data processing jobs have precedence constraints that complicate decisions, since delaying an upstream "bottleneck" task to a low-carbon period also blocks downstream tasks, impacting makespan. In this paper, we show that carbon-aware scheduling for data processing benefits from knowledge of both time-varying carbon and precedence constraints. Our main contribution is PCAPS, a carbon-aware scheduler that builds on state-of-the-art scoring or probability-based techniques - in doing so, it explicitly relates the structural importance of each task against the time-varying characteristics of carbon intensity. To illustrate gains due to fine-grained task-level scheduling, we also study CAP, a wrapper for any carbon-agnostic scheduler that generalizes the provisioning ideas of PCAPS. Both techniques allow a user-configurable priority between carbon and makespan, and we give basic analytic results to relate the trade-off between these objectives. Our prototype on a 100-node Kubernetes cluster shows that a moderate configuration of PCAPS reduces carbon footprint by up to 32.9% without significantly impacting total efficiency.

The proliferation of social media platforms, recommender systems, and their joint societal impacts have prompted significant interest in opinion formation and evolution within social networks. We study how local edge dynamics can drive opinion polarization. In particular, we introduce a variant of the classic Friedkin-Johnsen opinion dynamics, augmented with a simple time-evolving network model. Edges are iteratively added or deleted according to simple rules, modeling decisions based on individual preferences and network recommendations. Via simulations on synthetic and real-world graphs, we find that the combined presence of two dynamics gives rise to high polarization: (1) confirmation bias —i.e., the preference for nodes to connect to other nodes with similar expressed opinions and (2) friend-of-friend link recommendations , which encourage new connections between closely connected nodes. We show that our model is tractable to theoretical analysis, which helps explain how these local dynamics erode connectivity across opinion groups, affecting polarization and a related measure of disagreement across edges. Finally, we validate our model against real-world data, showing that our edge dynamics drive the structure of arbitrary graphs, including random graphs, to more closely resemble real social networks. Our code and supplemental materials are available at https://github.com/adamlechowicz/opinion-polarization/ . 1

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. We formalize a practically-relevant notion of time fairness which effectively models a trade off between static and dynamic pricing in a motivating application such as cloud resource allocation, and show that existing algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness (static pricing) and competitiveness (dynamic pricing). We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in experiments. To further improve the trade-off between fairness and competitiveness, we develop a nearly-optimal learning-augmented algorithm which is fair, consistent, and robust (competitive), showing substantial performance improvements in numerical experiments.

We introduce and study a family of online metric problems with long-term constraints. In these problems, an online player makes decisions $\mathbf{x}_t$ in a metric space $(X,d)$ to simultaneously minimize their hitting cost $f_t(\mathbf{x}_t)$ and switching cost as determined by the metric. Over the time horizon $T$, the player must satisfy a long-term demand constraint $\sum_t c(\mathbf{x}_t) \geq 1$, where $c(\mathbf{x}_t)$ denotes the fraction of demand satisfied at time $t$. Such problems can find a wide array of applications to online resource allocation in sustainable energy/computing systems. We devise optimal competitive and learning-augmented algorithms for the case of bounded hitting cost gradients and weighted $\ell_1$ metrics, and further show that our proposed algorithms perform well in numerical experiments.

The proliferation of social media platforms, recommender systems, and their joint societal impacts have prompted significant interest in opinion formation and evolution within social networks. We study how local edge dynamics can drive opinion polarization. In particular, we introduce a variant of the classic Friedkin-Johnsen opinion dynamics, augmented with a simple time-evolving network model. Edges are iteratively added or deleted according to simple rules, modeling decisions based on individual preferences and network recommendations.