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As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a specific objective. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, with only a negligible loss in the objective. 

Generating and executing temporal plans is difficult in uncertain environments. The current state-of-the-art algorithm for probabilistic temporal networks maintains a high success rate by rescheduling frequently as uncertain events are resolved, but this approach involves substantial resource overhead due to computing and communicating new schedules between agents. Aggressive rescheduling could thus reduce overall mission duration or success in situations where agents have limited energy or computing power, and may not be feasible when communication is limited. In this paper, we propose new approaches for heuristically deciding when rescheduling is most efficacious. We propose two compatible approaches, Allowable Risk and Sufficient Change, that can be employed in combination to compromise between the computation rate, the communication rate, and success rate for new schedules. We show empirically that both approaches allow us to gracefully trade success rate for lower computation and/or communication as compared to the state-of-the-art dynamic scheduling algorithm.