Erlebach, ThomasThomasErlebachde Lima, Murilo SantosMurilo Santosde LimaMegow, NicoleNicoleMegowSchlöter, JensJensSchlöter2025-09-252025-09-252022https://media.suub.uni-bremen.de/handle/elib/22313https://doi.org/10.26092/elib/4264We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree problem, a fundamental combinatorial optimization problem that has been central also to the research area of explorable uncertainty. For all integral γ ≥ 2, we present algorithms that are γ-robust and (1+1/γ)-consistent, meaning that they use at most γOPT queries if the predictions are arbitrarily wrong and at most (1+1/γ)OPT queries if the predictions are correct, where OPT is the optimal number of queries for the given instance. Moreover, we show that this trade-off is best possible. Furthermore, we argue that a suitably defined hop distance is a useful measure for the amount of prediction error and design algorithms with performance guarantees that degrade smoothly with the hop distance. We also show that the predictions are PAC-learnable in our model. Our results demonstrate that untrusted predictions can circumvent the known lower bound of 2, without any degradation of the worst-case ratio. To obtain our results, we provide new structural insights for the minimum spanning tree problem that might be useful in the context of query-based algorithms regardless of predictions. In particular, we generalize the concept of witness sets - the key to lower-bounding the optimum - by proposing novel global witness set structures and completely new ways of adaptively using those.enhttps://creativecommons.org/licenses/by/4.0/explorable uncertaintyqueriesuntrusted predictions000 Informatik, Informationswissenschaft, allgemeine Werke::000 Informatik, Wissen, SystemeText::Konferenzveröffentlichung::Tagungsband::Konferenzbeitrag10.26092/elib/4264urn:nbn:de:gbv:46-elib223130