We initiate the study of deterministic distributed graph algorithms with predictions in synchronous message passing systems. The process at each node in the graph is given a prediction, which is some extra information about the problem instance that may be incorrect. The processes may use the predictions to help them solve the problem. The overall goal is to develop algorithms that both work faster when predictions are good and do not work much worse than algorithms without predictions when predictions are bad. Concepts from the more general area of algorithms with predictions, such as error measures, consistency, robustness, and smoothness, are adapted to distributed graph algorithms with predictions. We consider algorithms with predictions for distributed graph problems, where each node is given a prediction for its output. We present a framework for evaluating distributed graph algorithms with predictions and methods for transforming existing algorithms without predictions to effectively use predictions. Our approach is illustrated by developing algorithms with predictions for the Maximal Independent Set problem. We also include a discussion of error measures and demonstrate how fine-tuning an error measure towards a particular problem can yield stronger results about the performance of algorithms for that problem.

翻译：我们在同步消息传递系统中开创性地研究了确定性分布式图算法与预测的结合。图中每个节点上的进程被赋予一个预测，这是关于问题实例的一些额外信息，这些信息可能不正确。进程可以利用这些预测来帮助解决问题。总体目标是开发出在预测良好时运行更快、在预测不佳时性能不会比无预测算法差太多的算法。我们借鉴了更广泛的带预测算法领域中的概念，如误差度量、一致性、鲁棒性和平滑性，并将其适配到带预测的分布式图算法中。我们研究了针对分布式图问题的带预测算法，其中每个节点都获得关于其输出的预测。我们提出了一个评估带预测分布式图算法的框架，以及将现有无预测算法有效转化为利用预测的方法。我们通过为最大独立集问题开发带预测算法来展示该方法。我们还讨论了误差度量，并展示了针对特定问题微调误差度量如何能够为该问题的算法性能带来更强的结果。