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Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty

Authors Thomas Erlebach , Murilo Santos de Lima , Nicole Megow , Jens Schlöter

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Author Details

Thomas Erlebach
  • Department of Computer Science, Durham University, UK
Murilo Santos de Lima
  • München, Germany
Nicole Megow
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany
Jens Schlöter
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany

Funding

  • Erlebach, Thomas: Supported by EPSRC grant EP/S033483/2.
  • de Lima, Murilo Santos: Work done while employed at University of Leicester, United Kingdom, and funded by EPSRC grant EP/S033483/1.
  • Megow, Nicole: Supported by the German Science Foundation (DFG) under contract ME 3825/1.
  • Schlöter, Jens: Funded by the German Science Foundation (DFG) under contract ME 3825/1.

Cite AsGet BibTex

Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter. Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 49:1-49:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ESA.2022.49

Abstract

We 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • explorable uncertainty
  • queries
  • untrusted predictions

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