The main bottleneck in designing efficient dynamic algorithms is the unknown nature of the update sequence. In particular, there are some problems, like 3-vertex connectivity, planar digraph all pairs shortest paths, and others, where the separation in runtime between the best partially dynamic solutions and the best fully dynamic solutions is polynomial, sometimes even exponential. In this paper, we formulate the predicted-deletion dynamic model, motivated by a recent line of empirical work about predicting edge updates in dynamic graphs. In this model, edges are inserted and deleted online, and when an edge is inserted, it is accompanied by a "prediction" of its deletion time. This models real world settings where services may have access to historical data or other information about an input and can subsequently use such information make predictions about user behavior. The model is also of theoretical interest, as it interpolates between the partially dynamic and fully dynamic settings, and provides a natural extension of the algorithms with predictions paradigm to the dynamic setting. We give a novel framework for this model that "lifts" partially dynamic algorithms into the fully dynamic setting with little overhead. We use our framework to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems. In particular, we design algorithms that have amortized update time that scales with a partially dynamic algorithm, with high probability, when the predictions are of high quality. On the flip side, our algorithms do no worse than existing fully-dynamic algorithms when the predictions are of low quality. Furthermore, our algorithms exhibit a graceful trade-off between the two cases. Thus, we are able to take advantage of ML predictions asymptotically "for free.''

翻译：设计高效动态算法的主要瓶颈在于更新序列的未知性。特别地，某些问题（如3-顶点连通性、平面有向图全对最短路径等）中，最佳部分动态解与最佳全动态解之间的运行时间复杂度存在多项式甚至指数级的差距。本文受近期关于动态图中边更新预测的实证研究启发，提出了预测-删除动态模型。在该模型中，边以在线方式插入和删除，每条边插入时都附带其删除时间的"预测"。这模拟了现实场景：服务可能获取输入的历史数据或其他信息，并据此对用户行为进行预测。该模型在理论上也具有重要意义，因为它动态地介于部分动态与全动态设置之间，并将"带预测算法"范式自然扩展至动态场景。我们为该模型设计了一个新型框架，能以极低开销将部分动态算法"提升"为全动态算法。利用该框架，我们为多种问题改进了现有最优动态算法的效率边界。特别地，当预测质量较高时，我们设计的算法能以高概率实现与部分动态算法规模相当的均摊更新时间复杂度；当预测质量较低时，算法性能不低于现有全动态算法。此外，算法在两种情况之间展现出平滑的权衡特性。因此，我们能够渐近地"免费"利用机器学习预测。