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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.49
URN: urn:nbn:de:0030-drops-169872
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16987/
Erlebach, Thomas ;
de Lima, Murilo Santos ;
Megow, Nicole ;
Schlöter, Jens
Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty
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.
BibTeX - Entry
@InProceedings{erlebach_et_al:LIPIcs.ESA.2022.49,
author = {Erlebach, Thomas and de Lima, Murilo Santos and Megow, Nicole and Schl\"{o}ter, Jens},
title = {{Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty}},
booktitle = {30th Annual European Symposium on Algorithms (ESA 2022)},
pages = {49:1--49:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-247-1},
ISSN = {1868-8969},
year = {2022},
volume = {244},
editor = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16987},
URN = {urn:nbn:de:0030-drops-169872},
doi = {10.4230/LIPIcs.ESA.2022.49},
annote = {Keywords: explorable uncertainty, queries, untrusted predictions}
}
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Keywords: |
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explorable uncertainty, queries, untrusted predictions |
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Collection: |
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30th Annual European Symposium on Algorithms (ESA 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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01.09.2022 |
