We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the $\ell_1$ error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to $\mathrm{poly} \log n$ factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between $\ell_1$ error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, $k$-edge connectivity, and others, for prediction error of reasonable magnitude.

翻译：我们提出预测更新动态模型，这是动态算法领域首批突破最坏情况假设的模型之一。该模型将包括离线动态、增量与减量模型在内的大量经典动态模型推广至完全动态场景，在给定元素更新时间的预测信息时生效。模型最基本形式中，我们接收事件时间跨度内所有更新的预测时间集合。给出一种新颖框架，能以极低开销将离线分治算法"提升"至完全动态场景。利用该框架，我们能够在离线与完全动态场景间进行插值：当预测的$\ell_1$误差与更新次数呈线性关系时，算法可实现离线运行时间（至多$\mathrm{poly} \log n$因子）。若存在完全动态后备算法，无论预测误差如何，本算法性能始终不低于该后备算法。此外，框架实现了预测$\ell_1$误差与运行时间之间的平滑线性权衡。这些性质分别对应算法预测文献中一致性、鲁棒性与优雅降级的三项需求。我们进一步将技术扩展至增量与减量场景，在仅知删除时间或插入时间预测时实现算法转换。本框架具有通用性，我们将其应用于三连通性、平面有向图全对最短路径、$k$边连通性等多个问题，在合理量级的预测误差下，其结果的状态最优动态算法均取得效率改进。